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TENSION gNVCtOPI CORP.
/'A-
KANSAS CITY. MO PUBUf 1 HfUM>
DOD1
PHYSICS OF THE TWENTIETH CENTURY
PHYSICS
of the
20 TH CENTURY
By
PASCUAL JORDAN
Translated by
ELEANOR OSHRT
PHILOSOPHICAL LIBRARY
NEW YOBK
Copyright 1944
By
Philosophical Library, lac,
15 East 40th Street, New York, N. Y.
Printed in the United States of America
by
R Hubner & Co., Inc.
New York, N. Y.
CONTENTS ;?>;
PAGE
Preface ............................. . ...... vii
Chapter I
Classical Mechanics ...................... 1
Chapter II
Modern Electrodynamics . . ............... 24
Chapter III
The Reality of Atoms .................... 51
Chapter IV
The Paradoxes of Quantum Phenomena .... 83
Chapter V
The Quantum Theory Description of Nature. . Ill
Chapter VI
Physics and World Observation .......... . 139
Appendix I
Cosmic Radiation .......... , ............ 166
Appendix II
The Age of the World ............ . .' ...... 173
PREFACE
This book tries to present the concepts of
modern physics in a systematic, complete review.
The reader will be burdened as little with details
of experimental techniques as with mathematical
formulations of theory. Without becoming too
deeply absorbed in the many, noteworthy details,
we shall direct our attention toward the decisive
facts and views, toward the guiding viewpoints of
research and toward the enlistment of the spirit,
which gives modern physics its particular phil
osophical character, and which made the achieve
ment of its revolutionary perception possible. First,
we shall review the classical Galilean-Newtonian
mechanics. A thorough appreciation of this is
prerequisite to any understanding of the revolu
tionary developments of modern physics. Through
the development of Maxwellian Electrodynamics
we shall arrive at the modern views both in
macrophysics and microphysics of atoms, elec
trons and quanta.
That modern physical research led to revolu
tionary changes in the traditional concepts of the
natural sciences is by no means a new idea. The
provocative appeal of these wonderful develop
ments was not the only reason I felt it desirable
to write this book, I was anxious, also, to aid in
the gradual removal of misunderstandings of the
newest developments in physics displayed by many
laymen. Continuation of such misconceptions can
vii
TWENTIETH CENTURY PHYSICS
lead to disturbing confusion. Thus, In the public
mind, entire chains of misunderstandings have
arisen through a fallacious combination of ob
jective scientific questions with wholly different,
e.g., purely personal ones. Even after the correc
tion of the gross errors many doubts and obscuri
ties still remain.
Laymen have frequently regarded as a sign of
doubt and confusion the fact that even the funda
mentals of the previous scientific world-picture
have become limited in their validity; that con
cepts such as space, time, causality have become
subject to incisive revisions. They maintained
that the new basic fundamentals suggested vacil
lations, that a threatening crisis had broken out
or that unrestrained dogmatism and uncertainty
had spread. The newly disclosed phenomena liber
ated us from outmoded, traditional concepts, thought
processes and ideas. This liberation is only a neces
sary prerequisite for the tremendous growth of our
knowledge and understanding which has already
begun. The certainty and permanence of our
physical science lies in the experimental facts.
Here there is no renunciation and reformulation
of things already established. Here there is only
progressive development of new ideas. The con
cepts and mental pictures to which we made the
facts of the narrower, previously explored domain
conform, can be proven insufficient by the broad
ening of our factual knowledge. Our most won
derful moments of scientific evolution are ex
perienced when it is shown that we must revise our
ideas from the ground up to agree with a new con-
vtu
TWENTIETH CENTURY PHYSICS
cept. Modern physics effected many such changes;
and in the most fundamental respects. That is
what this book would like to tell about.
When, in the preceding paragraph, we sum
marized what these developments yielded in prin
cipled, philosophical information, it seemed natural
that from our newly gained position we would
undertake a reexamination of the picture of the
physical world as well as of the meaning of non-
physical questions.
Certainly the religious question cannot be
avoided here. Bavink, in a very noteworthy way,
attempted by means of the insight of the new
physics to present a new answer to the old prob
lem of the relation of natural science and religion;
it seemed worthwhile to me to further investigate
the relation of the scientific theoretical philosophi
cal standard being expressed in modern physics to
Bavink's ideas.
It was inevitable that the author's personal
judgement should assume some weight in the
choice of facts and questions discussed, in the
discrimination between important and unimpor
tant concepts, in many an outline of a reported
development of ideas, and in the philosophical
evaluation of methods of reasoning and results,
It was my endeavor, however, to limit the
description as strictly as possible to things which
were scientifically proven and independent of per
sonal opinion; thus to include only proven experi
mental facts reported by leading, authoritative
investigators whose opinions are a reliable basis
for drawing conclusions and knowledge.
ix
TWENTIETH CENTURY PHYSICS
This strict limitation forced me to cease consid
eration at the point where it led to questions out
side of the boundaries of physics questions en
countered and placed in a new light because of the
revolutionary change of our physical conception of
the world. In three points especially this neces
sity applies:
1. In the investigation of the relation of
modern physical research to the religious question
any positive conclusion about religious possibili
ties must be supplemented by an acceptance of
the possibility of the validity of the former anti-
religious position of science. The reader will not
be able to recognize whether the author personally
inclines toward an historically old or a modern idea
of religion although actually, the author has a
very definite personal opinion on this subject.
2. Likewise, it would be overstepping the above
designated bounds to discuss the question of the
deeper, spiritual relationship between the revolu
tion in physical thought and knowledge described
in this book and the far-reaching changes which
are taking place in the whole world outside of
science. To me, modern physics and its accom
panying revolution in century old conceptions of
physical science is an integral component of the
unfolding of the new world of the twentieth
century.
3. Finally, it seemed worthwhile to include just
a short reference to an important field of thought
which really belongs within the realm of pure
science, but not strictly within the boundaries of
physics. This is the problem which has been
TWENTIETH CENTURY PHYSICS
raised in biology by the changes and the extension
of our physical knowledge. Despite the skepticism
with which my ideas on this subject
book]} were appraised by many biologists, one of
the most important biological theses which I indi
cated as probable has just recently been verified ex
perimentally : Timof eef-Ressovsky, Zimmer and
Delbriick showed that genes are molecules and
that mutations are elementary quantum-physical
processes. The wonderful insight almost simul
taneously arrived at that virus individuals, like
genes, are nothing but single molecules (Stanley),
strengthened the proof of my biological-atomic physi
cal theory. On the basis of the extensive experimen
tal material, which was compiled through the inves
tigation of the biological effects of radiation, I
could briefly prove the general usefulness of an
atomic-physical and quantum-physical interpreta
tion of the elementary life processes (in the sense
of my "Theorjr^^
But a presentation of this matter would be going
too far beyond the framework of this book.
Just a third of our century of physical re
search, opened by Planck's discovery of quanta
(1900), has elapsed and physics presses forward
at a tempestuous rate toward new discoveries
and conquests. It may therefore appear pre
sumptuous to speak already of a "Physics of the
Twentieth Century", But two things appear to
me to leave no room for doubt: first, that the
consummated revolution of our scientific knowl
edge is not to be made retrogressive by future
new discoveries. And secondly, no matter how
ad
TWENTIETH CENTURY PHYSICS
far beyond present attainments the future decades
lead, the discovery of Planck's quantum of action
must in the future also remain recognized as the
historical breaking point at which the epoch of
scientific research which began with the Rennais-
sance ended, and a new epoch was opened.
, p T
JT. J.
xii
CHAPTER I
CLASSICAL MECHANICS
1. Macro physics and Micro physics. Modern
physics accepts the atomic structure of matter. Mat
ter, palpable and visible to us, is made up of large
numbers of minute bodies, called atoms, which can
neither be seen nor felt Greek philosophers
had suspected the existence of atoms, and this con
cept taken over from the Greeks has played an im
portant part in scientific investigation and develop
ment since the beginning of western scientific re
search. But it was not until this century that what
had been supposition, speculation or fantasy was
raised to the rank of solidly established scientific
knowledge confirmed by direct experimental proof.
It can even be said that ours is the century of
atomic research in physics; and a survey of the
ideas of modern physics should first of all deal with
the investigation of atoms.
But the first two chapters deal with those fields
of physics which do not involve any discussion of
atoms. For the moment, let us consider a piece of
homogeneous matter capable of being subdivided.
A piece of copper or a piece of rock crystal can be
broken and split up into smaller and smaller pieces,
and the fragments continue to show the character
istic properties of the copper or the quartz. Even
if certain limits existed for the practical accom
plishment of such a subdivision it is difficult to
break up into smaller parts quartz which has already
1
TWENTIETH CENTURY PHYSICS
been ground tip to dust yet this rough experiment
presents no criterion for the existence of a definite,
clear limit to further subdivision. The dust par
ticles still differ in size and shape among themselves.
Thus one might conclude, that even though our
tools are ineffective nature presents no obstacle
to halving the smallest dust particle once more,
and to halving" this half again, and so on. . . without
a limit.
Today we know with certainty that that is false.
But very refined methods are required to attain
the limit to the continued division of matter in
other words, for the experimental determination of
the atomic structure of matter. But, as previously
stated, such methods have been available for only
a few years. Thus there are large and rich fields
of physical research in which the atomic structure
of matter is not at all recognizable. Naturally no
information about atoms can be expected from such
research, but then no knowledge of atoms is neces
sary, as long as investigation is limited to these
fields. It is customary to speak of macroscopic
physics (or macrophysics) when referring to those
investigations in which the presence of atoms is not
discernible; on the other hand research which
penetrates into the atomic detail of matter is denoted
as microphysics.
This review is devoted in large part to a discus
sion of microphysics but since only a thorough
comprehension of macrophysics can make possible
an understanding of microphysics, we shall begin
with a discussion of the former. Moreover, it was in
our century that macrophysics reached its final ma-
TWENTIETH CENTURY PHYSICS
turity, and therefore several of its chapters also
form an extremely modern science. It was in these
recent developments that certain philosophical theo
retical thought processes were developed and clari
fied, making it possible to reconcile the surprising
and paradoxical results of microphysical experi
ments, which previously were difficult to under
stand.
We are beginning with very simple things.
Despite their simplicity, however, they merit careful
and thoughtful consideration.
2, The Laws of Falling Bodies. The Greeks
had already established the laws of statics, of
mechanical equilibrium of levers and of fluids. The
essentials of these laws had been clarified. On the
other hand, dynamics, the theory of the mechanical
laws of motion, was first established by Galileo.
It is not within the province of this review to trace
the historical development of Galileo's investiga
tions; although for a deeper spiritual historical
understanding of modern science, closer considera
tion of the historical origin of modern physical
thought up to the end of the Middles Ages would
be very valuable. We shall simply consider Galileo's
laws of falling bodies in their finished form. The
simplicity of these laws and the ease with which they
can be interpreted today should not deceive us as
to how tremendous was his mental capacity. To
judge his contributions fairly, the historical-cultural
background and the ideas so completely changed
and readjusted since then prevalent in pre-Galilean
times should be considered.
Let us consider the motion of a falling or pro-
TWENTIETH CENTURY PHYSICS
jected body. Simple, everyday experience indicates
that a feather falls more slowly than a piece of lead;
and Aristotle had taught generally that light bodies
fall more slowly than heavy ones. Galileo's main
contribution is that he recognized the possibility of
extracting an obscure but simple law from the
amazingly complicated motions of real projected
bodies; he considered falling motion in a vacuum.
It is possible to prove that in an evacuated tube a
feather falls as quickly as a piece of lead this
experiment is part of the course of study in schools
today. But Galileo's contemporaries still considered
the Idea of a vacuum as Impossible, as nonsense. In
those times it required far greater strength of intel
lectual abstraction than we might expect today, to
recognize that it was possible to separate (mentally)
all the associated events from the motion of falling
bodies. We know today that the effects which orig
inate from atmospheric pressure and the influence
of the wind can lead the motion of a falling feather
to proceed entirely differently from that of a falling
stone.
But it is possible to extract from all these com
plex and varied motions an ideal form which is to
be regarded as the motion of a body in a vacuum.
This "ideal" projectile motion is wonderfully simple
compared to the actual motions of falling bodies or
projectiles :
1. Ideal projectile motion is always a plane mo
tion (proceeding within a fixed plane perpen
dicular to the earth's surface).
2. It proceeds independently of the mass, size
and shape of the projected body; it simply
TWENTIETH CENTURY PHYSICS
depends upon the magnitude and direction of
the initial velocity.
3. It is not influenced by any rotation of the
projectile around its own center of gravity;
even if the body rotates around it, this center
of gravity moves according to the law of ideal
projectile motion.
These properties do not properly describe the
motion of a real bullet, which is not exactly a plane
motion, and which depends very substantially on
the mass, size and shape of the projectile as well
as on its spin (rotation).
Here we witness one of the historically most
important examples of physical natural scientific
thought. The phenomena presented to us directly
by nature are so varied and complex that it is
impossible for our narrow minds to grasp them
individually. We must mentally divide these natural
occurrences into their simpler components ; we must
consider results of artificially produced extremely
unnatural conditions instead of those offered through
direct experience. Thus we uncover the ideal cases,
which can be subjected to more precise, considered
treatment. These results in turn establish criteria
for the evaluation of the real events, in each case
different from the ideal to a greater or lesser extent
Now let us consider the laws of ideal projectiles
more exactly. For this we want to view the simplest
case, namely vertical rectilinear fall. The body,
first retained at rest and then released, falls down
wards as long as it continues to fall with ever
increasing velocity. At the instant of release, the
velocity is exactly zero, but thereafter it increases
5
TWENTIETH CENTURY PHYSICS
steadily. This increase does not proceed in inter
mittent, rapidly repeating, sudden jumps, but rather
in an uninterrupted, continued growth, in which
there are neither pauses nor sudden discontinuities.
Mathematicians express it very clearly when they
say that the velocity increases uniformly.
In such a case, when the velocity is changing uni
formly and constantly so that it is never the same
at two different points in time, no matter how
closely they may follow one another, what does
velocity mean?
When a body moves with uniform velocity it is
clear what velocity means the distance traversed is
divided by the time of travel We commonly say
that a body traveled at a velocity of one meter per
second or that an auto traveled at seventy kilo
meters per hour. But how are we to understand
and define velocity abstractly if it doesn't remain
fixed throughout even a fraction of a second?
In Galileo's times this question presented very
great difficulty ; the abstract and mathematical tools
for solving it were still lacking. In an evaluation
of Galileo's contributions, this fact, too, must be
remembered. Galileo had been able to dispose of
these questions completely for ideal projectile mo
tion; it only became evident later how great an
achievement this was. Newton cleared up the con
cept of velocity (and acceleration) quite generally,
for any motions. For this purpose he had to estab
lish an entirely new branch of mathematics, the
so-called differential calculus.
Differential calculus (including the chapters of
mathematics connected with it) is undoubtedly the
TWENTIETH CENTURY PHYSICS
greatest creation achieved by western mathemati
cians. In this Leibnitz stands beside Newton as the
founder although his considerations did not eman
ate from mechanics, but rather from geometry.
Naturally both of them, Leibnitz and Newton, re
ferred back to forerunners and trailblazers ; in the
problems of their time and in their natural scientific
and mathematical investigation there lay an inevi
table compulsion toward this direction of thought.
But what they produced by bold statements occupied
generations of mathematicians after them and stimu
lated further great results.
This new mathematics, which is an original
creation of western thought, not anticipated by the
Greeks, deals with precisely those questions which
confront us when we inquire about the exact mean
ing of the "concept" of velocity in the case of con
stantly changing velocity. The function of differen
tial calculus is to express clearly mathematically
quantities that describe constant, fluid, continuous
change. For this reason the idea of continuity is
the central, controlling concept, around which the
thought paths of this chapter of mathematics
revolve.
The exact definition of velocity can be expressed
as follows. First, it is clear what is meant by the
average velocity within a given time interval the
distance traveled in this time is divided by the
length of time. Now, in order to obtain the exact
velocity for a given point in time we choose a small
time interval (including this point in time) and
determine the average velocity associated with this
interval; it will, if the time interval chosen is small
TWENTIETH CENTURY PHYSICS
enough, give an approximately correct value for the
exact velocity desired. This value can be improved
by replacing the time interval with one half as large;
and then this improvement can be repeated. It is
frequently possible to repeat it mentally at pleasure,
and thus with unlimited approximations to approach
ever more exactly the precise value desired.
This, therefore, is the definition of the concept
of "velocity". The problem is no simpler if one
wants to obtain the results quantitatively, and for
this purpose wants to sharpen the concept so that
it will make a mathematical evaluation possible
when one does not want to be content with a solely
emotional, indefinite application of the concept. But
one need not fear that this has led to a hopeless,
practically insoluble problem in calculation. On
the contrary, there are ingenious considerations
(and their cultivation is the inherent content of
differential calculus) which make it possible to
establish in a specific form of motion the limiting
value which we must take as the basis for the
definition of velocity.
Galileo had already answered these questions for
ideal falling motion. He had recognized that for ,
this ideal motion, dissociated from air resistance
and all secondary influences, a wonderfully simple
law exists ; namely, velocity increases proportionally
with time. Thus, after double, triple, etc., time of
fall it is exactly doubled, tripled, etc.
This law extends also to general ideal projectile
motion. If we throw a body vertically upwards
or downwards, its downward velocity will still
always increase in proportion to time which in the
8
TWENTIETH CENTURY PHYSICS
case of upward motion naturally means a corre
sponding decrease in the upward velocity. If it is
thrown obliquely, the body's height measured ver
tically to the earth's surface (in ideal projectile
motion) changes with the passage of time exactly
as if it also were a vertical fall Simultaneously, the
horizontal distance from the starting point increases
proportionally with time; or expressed differently,
in the horizontal direction the motion proceeds with
fixed velocity. Mathematical consideration of these
determinations yields the fact that the projectile
path (trajectory) is a parabola.
3. Force and Motion. The laws of generalized
ideal projectile motion formed another example of
how scientific thought made natural processes com
prehensible through resolution into simpler com
ponents. We conceive of parabolic motion as
simultaneous execution of two different motions,
vertical and horizontal. It is also possible to study
the horizontal motion isolated from the vertical
for this all we need is a horizontal rail, or perhaps
a plane ice surface, on which the body can slide.
Then for the ideal limiting case (ie., in the case of
not only the absence of air resistance, but also of
any friction accompanying the sliding) we reach
the conclusion that the body moves in the horizontal
direction with constant velocity.
Galileo accepted the certainty of the spherical
shape of the earth, at that time not a very old concept;
and he could represent the earth as moving freely
through space on the basis of the Copernican theory
which he accepted. Thus he knew that the motions
horizontal and vertical or above and below are only
TWENTIETH CENTURY PHYSICS
relative. And from this the possibility of gener
ally recognizing the basic form of motion, free
from external influences, in the ideal, resistance-
free motion of a horizontally sliding body became
evident Newton, the first one to state this clearly,
expressed his famous law of inertia as follows: a
body moving in a vacuum unobstructed and free
from external forces moves in a straight line with
constant velocity.
Falling motion must thus be conceived as a devia
tion from the invariable behavior of a body, for
which the cause is to be sought in an attractive
force emanating from the earth, Newton clarified
for all cases the manner in which a force acting on
its center of gravity alters the motion of a body
the force manifests iteslf in a change of velocity,
an acceleration. In vertical free fall the acceleration
is constant whereby we define acceleration as the
increase in velocity divided by the duration of the
fall. For complex motion, in which the acceleration
is no longer constant but is subjected to continuous
changes the same considerations are necessary as
were introduced for the concept of velocity. New
ton's new mathematics, differential calculus, mas
tered all these problems with one stroke.
If we limit ourselves to rectilinear, uni-dimensional
motion, then according to Newton the acceleration
is exactly equal to the force divided by the mass
of the accelerated body. It depends on neither
size nor shape, nor material, color nor temperature
of the body, but on its mass alone*
The laws of three-dimensional motion are analo
gously simple and general. Here It is simply neces-
10
TWENTIETH CENTURY PHYSICS
sary to resolve the motion into three components,
acting in mutually perpendicular directions, whose
simultaneous execution yields the total effective
motion. If the force acting on the body's center of
gravity is resolved correspondingly, the above New
tonian law is valid for each of the three uni-dimen-
sional portions of the whole process.
This knowledge made possible a clear definition
of the concept of physical causality. The general
notion that nothing happens unless a definite cause
exists for it was elevated to a quantitative law: a
definite force acting on a body imparts a definite
acceleration to that body.
This point merits further consideration. To really
understand the significance and importance of the
ideas which constitute physics, we must always be
ready to refer back to previous concepts. Only in
this way can we realize how revolutionary such
thoughts were at one time, although they have be
come quite familiar and conversant to us.
As the most prominent feature of natural-physical
research we recognize the search for quantitative,
mathematically comprehensible laws. We must
remember that extreme idealization of natural
events is necessary to render this search successful.
Since, by eliminating air resistance, Galileo attained
the process of ideal fall, he was able to uncover
mathematically simple, beautiful, exact laws; and
conversely, these laws show that he looked for
the idealization in the proper direction.
Naturally calculations on the projectile trajec
tories of modern weapons do not yield these ideal
projection laws at all Such calculations require
11
TWENTIETH CENTURY PHYSICS
consideration of air resistance which also is intro
duced in a more or less idealized form. Ballistics,
which deals with these problems, is a special, highly
developed science whose outstanding practical sig
nificance needs no special emphasis. But the science
of ballistics had nothing new to add for the general
development of physical science, for the development
of physical thinking and ideas.
The idea of continuity, which attained its mathe
matical form in differential calculus, is important
for the clear understanding of motive processes.
We also want to make it clear immediately that this
continuity of natural events "natura non facit
saltus" was already evident in the elementary fact
that it was at all possible to speak of a definite
trajectory of a moving body. A body cannot reach
one place from another by jerks, suddenly dis
appearing here and emerging again there; it must
describe a continuous connected path between the
two. But why is that necessary? We know frotn
experience that it always is that way, but is there
a logical necessity that it cannot be otherwise?
These questions are not idly posed: we shall never
be able to understand microphysics unless we have
carefully examined such questions.
If we continue to consider macrophysics, it must
be realized that in this sphere the principle of
continuity is valid without exception. When a shell
explodes, the proposition holds that individual frag
ments can only change their positions through
continuous motion, rapid as it may be. Or in an
automobile accident the law obtains that each
body can only change its velocity continuously,
12
TWENTIETH CENTURY PHYSICS
never with "discontinuous", complete suddenness.
Also, the quantitative, mathematical definition
of mechanical causality, in which Galileo's and
Newton's knowledge culminated, is inseparably
bound up with the concept of continuity. For, it is
through Newton's law "force equals mass times
acceleration" that constant changes in velocity are
traced back to the forces which cause them.
4. Relative Motion. The knowledge expressed
in the law of inertia and in Newton's definition of
the operation of force was diametrically opposed
to earlier views. Previously the problem had been
viewed just in reverse explanations were being
sought for the fact that a hurled stone retains its
velocity after being released from the hand. It
was considered natural and understandable that it
must lose its velocity if the impulse is lacking to
maintain it. For everyday experience does indicate
that a wagon, for example, which is supposed to
move uniformly along a straight path, does require
a continuous uniform force from the beast draw
ing it
The now recognized fact that, exactly opposite,
an uninfluenced body retains its velocity without
any change the wagon on the road is not a valid
example of this because it is retarded by the action
of friction and that quite generally only accelera
tion, and not velocity, is determined directly by the
acting force, is related to certain very significant
problems, which were not fully solved until this
century. For the moment these problems are per
tinent only so far as they refer to the mechanics of
Galileo and Newton.
13
TWENTIETH CENTURY PHYSICS
Opponents of the Copernican theory of the mo
tion of the earth around the sun had introduced
the following objection: if a gun is shot vertically
upward, the shot falls down close to the gun. But,
they said, according to Copernicus, since the earth
has in the meantime moved along some distance,
the shot should have fallen down in an entirely
different place. This was impressively demon
strated in an experiment by Gassendi: he dropped
a stone from the tip of the mast of a rapidly travel
ing boat. It fell down below near the mast, not
on the stern of the boat nor behind the boat in
the water.
Galilean-Newtonian mechanics explained this
result without more ado. And, since generally it
predicted suitable results for all analogous experi
ments, it lent an indispensable contribution to the
justification of the Copernican theory. To our
present thoughts, which accept the ideas of Galileo,
Newton and their associated mechanics as a basis,
the process is clear immediately: the stone, first
held in place at the tip of the mast and then released,
received the same velocity in the horizontal direc
tion as the boat; and it retained this horizontal
velocity (as long as the effect of air resistance was
negligible) so that as it fell downwards it moved
along with the ship in the horizontal direction.
From the Newtonian laws of mechanics it is
obvious that if a boat (or train) is traveling in a
straight line with constant velocity, one cannot
determine on the inside of a closed cabin of the
ship whether or how fast the boat (train) is travel
ing. Although naturally it can be deduced from the
14
TWENTIETH CENTURY PHYSICS
altered rocking of the boat or swaying of the train,
here we are considering the ideal case of a vehicle
moving along smoothly without rocking or bumping.
An object dropped in the cabin will fall vertically
to the floor, precisely as it obeys the law of falling
bodies on land. Now let us consider that an
observer standing on shore can see inside of the
cabin. The author desires to establish that the
falling object is still subject to the laws of falling
bodies, although this observer would not see it fall
vertically, but in a parabola with a horizontal
velocity (as long as the effect of air resistance was
that of the boat).
The concept of velocity is relative. The observer
on shore views all objects in the cabin with a
different velocity than the experimenting traveler;
for the witness on land every object moving in the
cabin acquires in its motion also the additional
velocity of the vessel. Therefore, to avoid mis
understanding we must always append to the word
velocity "relative to the boat" or "relative to land".
When a boat travels with constant velocity (rela
tive *to shore) then the acceleration of any body
relative to the ship is always the same as it is
relative to land despite the difference between the
relative velocities. Consequently the same mechan
ical laws apply to motion relative to the boat and
relative to land. In both reference systems the
same accelerations are caused by the forces acting.
This discovery, that one can never determine
uniform motion of a closed room from its inside
with any mechanical apparatus be it simple or
complex whose method of operation is subject to
15
TWENTIETH CENTURY PHYSICS
Newton's laws, is called the principle of relativity.
The principle of relativity is, beside the principle
of the conservation of energy, the most general and
most comprehensive physical law that we know*
As yet we have only established its validity with
respect to the laws of Galilean-Newtonian mechan
ics. But we shall see that its significance extends
far beyond this and embraces all fields of physics.
Therefore we can't perceive through any mechan
ical experiments conducted on the earth that the
earth (relative to the sun) glides along thirty
kilometers per second, or that the sun (relative to
the milky way system) flies along with still greater
velocity. And we can't distinguish whether the
milky way, which despite its tremendous size is
only a small island in space, for its part executes
as a unit any uniform rectilinear motion. The rota
tion of a body, for example, can be recognized by
means of mechanical effects. Anyone sitting on a
carousel can tell, even with his eyes closed, that
it is turning from the centrifugal force which
presses his body against the outer wall since
according to the law of inertia the body would fly
out in a tangential direction due to the rotary
motion if the outer wall didn't retain it. In the
same way we notice a curve within a train; we also
notice the acceleration or deceleration of rectilinear
motion when starting or stopping. It is only uni
form progression which is not noticed, because only
there is the acceleration of the body relative to the
vehicle the same as that relative to the fixed rails*
In the case of our earth the centrifugal force
caused by its rotation is evidenced in the flattening
16
TWENTIETH CENTURY PHYSICS
of the poles. It is also possible to measure the
earth's rotation directly through a simple mechan
ical experiment whereby the Copernican concep
tion of motion in our solar system, developed from
astronomical knowledge, was shown to be a neces
sary result of Newtonian mechanics. This is the
famous Foucault pendulum experiment. A weight
swinging on a very long thread transferred into an
elliptical form of vibration under the influence of
the earth's rotation. The measurement of this
effect permits the determination, based on Newton
ian mechanics, that the earth actually rotates with
the same speed that the "fixed star" sky seems to
move (oppositely directed) ; that actually the "fixed
star" sky, as Copernicus taught, remains at rest.
5. Newton's Law of Gravitation. The most
significant addition that Newton made to Galileo's
knowledge was his teaching that the motions of
the planets, conceived in the Copernican sense, were
to be considered as consequences of the same
mechanical laws which were derived ! from terres
trial falling motion. Newton availed himself of
the opportunity to demonstrate conclusively his
extension of Galileo's ideas, using as an example
the most wonderful mechanical system provided
by nature. To his admiring contemporaries the
explanation of known processes made possible by
the new mechanical principles was convincing proof
of the validity and profundity of these principles.
It was not exaggeration when H. Poincare once
said that mankind had learned mechanics from
celestial and planetary motions.
To his general mechanical laws, valid for all
17
TWENTIETH CENTURY PHYSICS
effects of mechanical force, Newton added the law
of gravitation: any two bodies exert an attractive
force on each other that is proportional to the
product of the two masses (thus, is doubled, tri
pled . . . with the doubling, tripling ... of either
mass), and that becomes weaker as the separation
between the two bodies is increased. The decrease
in attractive force with distance is such that, e.g.,
the attractive force of the sun on a meteoric stone
in interstellar space decreases with increasing sep
aration from the sun in the same manner as the
strength of the light emanating from the sun,
which becomes increasingly thinned out with in
creasing separation. Mathematically expressed, the
force of gravitation varies inversely as the square
of the distance/
Newton, by mathematical reasoning, showed that
the laws of the motions of the planets (discovered
by Kepler) are a necessary result of the gravita
tional attraction between the sun and the planets.
The Keplerian laws state:
L The orbit of each planet is an ellipse with
the sun at one of its foci.
2. Each planet revolves so that a line joining
it to the sun sweeps over equal areas in equal
intervals of time so that when the planet
is closer to the sun it moves more rapidly
than when it is at a more distant point in
its orbit.
3. The squares of the periods of any two plan-
1 This illustration, comparing the mathematical law of the
force of gravitation with light, should not he construed to
mean that a closer connection exists between these two phe
nomena.
18
TWENTIETH CENTURY PHYSICS
ets are in the same proportion as the cubes
of their mean distance from the sun.
It is obvious that Kepler's laws differ in nature
from the mechanical laws which formed the basis
for their final mathematical proof. Actually, Kep
ler himself viewed his laws in a manner different
from Newton's. For Kepler, his laws were pri
marily an expression of the beauty and harmony of
the divine creation; whereas Newton's laws
demonstrated in the planetary system the principle
of causality in nature, according to which the re
sultant motions proceed necessarily from the acting
forces.
This same gravitational force which regulates
planetary motions also determines the orbit of our
moon around the earth, or of her moons around
Jupiter. This same force which controls the solar
system with its planets, comets and moons is also
responsible for the fall of bodies on the earth.
In 1666 Newton had already visualized this com
prehensive picture of the validity of his law of
gravitation. But the calculations did not agree with
observations, The magnitude of the earth's attrac
tion working on the moon calculated from the mo
tion of the moon did not appear to correspond in
the sense of the Newtonian law with the magnitude
of the force of gravity at the earth's surface.
Newton concluded therefore, that still other forces
come into play here; and unsatisfied, he set this
investigation aside.
Not until sixteen years later, when he learned
that new geodetic measurements of the circumfer
ence of the terrestrial globe had yielded a value
19
TWENTIETH CENTURY PHYSICS
about one-sixth greater than had been accepted
until then, did he resume this work. Now New
ton's calculations agreed with observations. Four
years later, in 1686, his great work "Philosophise
Naturalis Principia Mathematica" appeared. In it
he developed the principles of mechanics, set up
the law of gravitation and taught the mechanics of
the planetary systems to be understood on these
bases ; he also explained the phenomena of the tides.
Shells from modern guns that shoot beyond 100
kilometers have projectile paths whose calculation
must include the consideration that the earth is not
flat, but is a sphere. Technology thus began to
bridge the wide chasm which was opened by New
ton's boldness of mind when he recognized that the
motions of the moon around the earth and the
planets around the sun are dependent upon the
same laws as projectile motion on the earth's sur
face. Newton bridged this gap in the following
hypothetical experiment : a projectile is shot off from
a high mountain somewhat horizontally. The ex
periment is performed repeatedly, with ever in
creased projectile velocity. The projectile strikes
ground farther and farther away ; when the velocity
is sufficient, at the other side of the earth; and with
still greater velocity the case is reached wherein
the projectile, by flying around the earth, again
reaches the point from which it was shot off. In
the "ideal" case of absence of air resistance
which condition actually prevails in interstellar
space where the planets, move around the projectile
will have maintained its initial velocity ; consequent
ly it will describe the same path again; and con-
20
TWENTIETH CENTURY PHYSICS
tinning, it will circle the earth permanently.
A characteristic feature of physical research can
be detected in this Newtonian extension to plane
tary mechanics of Galileo's investigation of pro
jectile motion. After obtaining a sure footing in
a limited field an attempt is made to transcend the
existing boundaries with the conceptions gained in
the immediate field serving as a basis for the inves
tigation of the more remote.
By trying to find connection and similarity be
tween the newer phenomena and those previously
investigated, an extension and generalization of
ideas and recognized laws can be reached. Such
generalized laws make it possible to "understand"
the entire, extended sphere of experience.
We have just placed the word "understand" in
quotation marks in order to emphasize the import
ance and profundity of the problem of being clear
about what is really meant by "understanding"
physical events and what goal is really striven
towards in physical investigation and search for
knowledge. Newton's celestial mechanics prob
ably on the whole the greatest contribution of phy
sical thinking ever accomplished indicated clearly
that "understanding" means nothing else than trac
ing back the new to the already known. Aristotle's
question, why a body that has been set in motion
retains its velocity, was not answered, but simply
brushed aside. The law of inertia establishes that
a body invariably and indefinitely retains its velocity
as long as retarding forces do not act upon it
And once one is satisfied with this establishment
that is not to be "understood", but simply accepted
21
TWENTIETH CENTURY PHYSICS
one also sees the problem of planetary motion
from an entirely new angle. One need no longer
(as Kepler still desired) assume in the sun the
seat of permanent impulsion of planetary motion.
One other point merits our attention before we
leave Newtonian mechanics for new subjects. What
are the results of the planets' mutual attraction
for one another? The mathematical solution of
this problem is extremely involved and difficult
(the famous "three body" problem). One fact is
c l ear s i nce the sun's mass is tremendously large
in comparison with the masses of the planets, the
attractive forces exerted on each planet by the other
ones are very weak in comparison with the attrac
tion of the sun. Thus it is understandable that the
Keplerian elliptical paths actually do prevail, with
only small deviations, weak "perturbations", caused
by the mutual effects of the planets on each other.
But shouldn't it be expected that these small
disturbances could grow with the passing of time
in such a way that they might change the magni
tude and positions of the elliptical orbits completely
in the course of millions of years, and the planets
would finally have to collide or plunge into the sun?
Newton entertained this suspicion. And he be
lieved that from time to time the world creator
must intervene to prevent such destruction. There
fore it was of great significance for the internal
consolidation of the natural physical conception
that Lagrange and Laplace later showed by clever
mathematical proofs that the planetary system pos
sesses "stability" of itself on the basis of the New
tonian law. Therewith the idea was accepted that
22
TWENTIETH CENTURY PHYSICS
the paths of all events in the universe are controlled
in their entire sequence without exception by the
mathematically defined natural laws of physics.
23
CHAPTER II
MODERN ELECTRODYNAMICS
1. ff Action at a distance" and "field of force".
Newton's analysis of planetary motions had verified
the existence of a gravitational attraction which
varies inversely with the square of the distance.
The presence of this force could be deduced from
Kepler's laws, from the motions of the moon and
terrestrial projectiles, and from the mutual per
turbations of the planets, which were subjected to
detailed investigations by later astronomers and
mathematicians. But a further problem remained
the problem of whether a deeper insight into the
phenomena of gravitational attraction could be
achieved; the problem of somehow understanding
and deriving this attraction of gravity from more
basic causes.
The fact that Newton had left this question open
led many important physicists of his time notably
Huyghens to mistrust the entire Newtonian
thought structure. Without a deeper, more ex
haustive explanation Huyghens refused to recog
nize Newton's formulation of the law of attraction
as satisfactory. At the other extreme, Newton's
admirers accepted the law of gravitational attrac-
tional as a final, independent world law that re
quired no further explanation. With this attitude
they did not, however, express Newton's own feel
ing; for he had never fundamentally denied the
justification of the demands for a firmer establish-
24
TWENTIETH CENTURY PHYSICS
ment of his law. However, he did state emphati
cally that he would be content with the determina
tion of the presence of this gravitational attraction
and the mathematical law for its quantitative de
scription. With this statement he ceased speculat
ing about its origins "Hypotheses non fingo".
The problem of the cause of the force of gravity,
which despite this remained an open problem for a
long time, could not lead any further at that time.
But a step ahead was possible with regard to a
similar physical law. Coulomb had shown that for
attractions and repulsions of electrical charges the
force is also inversely proportional to the square
of the distance of the mutually interacting charges.
Although here, in contrast to the attraction of
gravity, a known difference exists i.e., there are
two kinds of electricity, positive and negative,
wherein those of similar sign repel and opposites
attract yet, the mathematical law Newton discov
ered in the attraction of gravity also holds for
decrease of force with increasing distance. Physi
cists of the last century succeeded in obtaining a
deeper understanding of these electrical force
effects.
How can it be demonstrated that two electrical
charges exert forces on each other no matter how
far apart they may be? This "action at a dis
tance", this influence of one physical system on
another regardless of the distance between them
appeared unnatural to the physical intuition of the
investigator. The feeling that such a distant effect
could not be basic, but required an explanation and
a correlation with fundamentals doubtlessly resulted
25
TWENTIETH CENTURY PHYSICS
from the Influence of materialistic philosophy in the
course of historical development; its profound
effect on the thought development of western
natural science is an unmistakable historical fact
Materialistic philosophy, which taught that atoms
of matter, hypothetically introduced by it, were the
only seat of action, indicated that the reciprocal
effect of atoms through pressure and collision was
the only action properly explaining natural phe
nomena.
Thus it was necessary to explain the apparently
independent effects, widely separated from each
other, which are stated in Newton's and Coulomb's
laws, as results which somehow depended only on
pressure and collision of atoms.
Independently of these considerations, which to
day retain only historical significance, the acute
instinct of some investigators of the last century
led to the conviction that "action at a distance"
must be reduced to a "field of force" effect; that
the effects of a physical system could not extend
unaided over great distances; that each physical
effect must extend continuously in space from place
to place.
These convictions were firmly established by
Faraday and Maxwell. Faraday, the experimental
physicist, allowed his research to be governed by
original, new conceptions which in the course of
his wonderfully rich experimental discoveries un
derwent progressive development and verification.
These concepts contrasted radically with the ideas
of his contemporaries, still entirely built around
the principle of "action at a distance". Maxwell
26
TWENTIETH CENTURY PHYSICS
was the first to extend Faraday's ideas to include
the quantitative- wording and mathematical clarity,
which they lacked originally.
According to the concepts of this "field of force"
theory the reciprocal effects between electrical
charges are spread out through the intervening
space. Faraday's experiments had shown that these
reciprocal force effects were influenced and changed
by the presence of dielectrics anywhere within
the intermediate space. The idea was firmly
established logically that the space between the
apparently independent reciprocally acting elec
trical charges is really a carrier of the potentials
and energies distributed in it. These potentials
and energies are not directly perceptible to us, but
appear in the form of the forces which were de
scribed quantitatively by Coulomb's law.
Accordingly vacuum, "empty space", is also a
carrier of potentials and energies, the presence of
which is not bound up with the presence of matter.
Through this consideration Coulomb's law, mathe
matically expressed, was shown to be an "integral
law" which follows mathematically from "differen
tial laws". Coulomb's law appears as the result, as
the final effect of more primitive laws which refer
to the "field", i.e., to space filled up with electrical
potentials. Of course it is true that these laws,
simpler to interpret physically, require very much
more difficult mathematical tools for their formula
tion and exact understanding than does Coulomb's
law, so simple to express. It must be -established
k ere j n a wa y which emphasizes the principle of
continuity how the state of the electromagnetic
27
TWENTIETH CENTURY PHYSICS
field at a given point is related to its immediate
neighborhood, and how this electromagnetic state
at each point in space and in its immediate neigh
borhood acts to produce variations in potential with
time at that place (time rate of change).
2. Electromagnetic Waves. It follows logically
from the field of force theory that a definite amount
of time is necessary for the propagation of elec
trical effects. The assumption of an absolute dis
tance effect permits the following representation.
When an electric charge, which is acting on another
far removed charge according to Coulomb's law,
is suddenly displaced to another position, then in
stantaneously, without delay, the other, distant
charge will experience the modified effect of the
force, which corresponds to the new position. The
latter charge "notices" at once that the position of
the former one has been changed. But this idea
of an instantaneous propagation of physical effects
is incompatible with the idea of a "field of force".
If the action of the force exerted by the first charge
on the other remote one is effected through the
intervening space reaches the distant charge via
the bridge of potentials filling the space between
them then only the field the bridges in the
immediate vicinity of this charge will be modified
to correspond to its new, rapidly changing position.
This rearrangement of the field, which commences
in the neighborhood of the charge, spreads out into
space very rapidly. Nevertheless a finite time is
required before this modification extends to the
region of the other charge.
The electrical effects of a charge require a finite
28
TWENTIETH CENTURY PHYSICS
time for their propagation. If now we consider
the case of a charge which not only undergoes a
single rapid change in position but is repeatedly
and continuously induced to swing back and forth,
then the electric field never returns to a static con
dition. The electric field is transferred into a state
of periodic vibration corresponding to the periodic os
cillation of the charge electric waves emanate from
the swinging charge. At this point the "action at a
distance" and "field of force" theories separate into
their experimentally verifiable conclusions. The
mutual actions of static charges can be interpreted
both in the sense of "action at a distance" and of
"field of force". Despite the essential difference
between the methods of representation, problems on
static charges always yield the same results. This
holds not only for mutual action of static charges
according to Coulomb's law but also for many other
complex processes in the rich realm of electrical
phenomena. The "action at a distance" theory is
consistent with Faraday's discoveries, and could
be extended in its range of usefulness with results
that agree with experimental facts just as well as
the "field of force" theory. It was only the asser
tions of the "field of force" theory regarding
electromagnetic waves, which are said to emanate
from oscillatory charges, that made a final decision
about "action at a distance" and "field of force"
possible, since these waves could not be reconciled
in any way with the idea of "action at a distance".
The history of physics contains no more impres
sive example of the creative force of theoretical
thought in physics than the history of the discovery
29
TWENTIETH CENTURY PHYSICS
of electromagnetic waves. For these waves, which
today rank among the most important problems and
media of technical work and which assume a note
worthy position in the general framework of our
modern life, were not discovered through experi
mental research. They were formulated on paper,
educed from the mathematical formulas which Max
well had begun to evolve as a quantitative descrip
tion of Faraday's ideas. Only subsequently were
they sought experimentally, and found by Hertz.
A more detailed treatment of Hertzian waves
would be superfluous. Originally the discovery of
a meditating theoretician, later observed by the
experimental investigator, these waves are today
familiar to the layman as a result of their technical
application in everyday life. Everyone knows
that radio waves have wave lengths that extend up
to several kilometers. Actually there are electro
magnetic waves of much longer wave lengths, but
practically these are of little importance. Short
wave transmitters utilize wave lengths of about a
meter; ultra-short wave (ultra-high frequency)
transmitters use wave lengths of the order of mag
nitude of a centimeter; and experimental results
show that infra-red heat rays are simply still short
er electromagnetic waves, whose wave lengths equal
only fractions of a millimeter.
On the basis of known experimental results,
Maxwell was able to determine theoretically how
great the propagation velocity of the electromag
netic waves he had predicted must be. His result
led him to a bold inference through which an entire,
hitherto independent chapter of physics was classi-
30
TWENTIETH CENTURY PHYSICS
fied under electrodynamics. Maxwell found that
the propagation velocity of electromagnetic waves
must be the same as the velocity of light; and he
concluded that light is actually a form of electro
magnetic radiation.
3. Light. Olaf Romer had determined the
velocity of light as early as 1675. In observations
that extended over several years he noted the
entrance of the innermost of Jupiter's moons into
the shadow cast by Jupiter and its emergence from
the shadow into the sunlight. If it is correct that
light requires a finite time to travel from one place
to another then the entrance of one of her moons
into Jupiter's shadow will not become visible on
the earth until somewhat later. Likewise a measur
able interval of time elapses before the sunlight,
begun to be reflected by Jupiter's moon upon its
^emergence from the shadow, reaches the earth. If
this moon, which requires 42^2 hours for each
revolution around Jupiter, maintained a constant
separation from the earth, its emergence from the
shadow would become visible to an observer on the
earth regularly every 42^ hours. But while the
moon has completed 30 revolutions, for example,
the earth has advanced in its orbit so that its
separation from Jupiter, and therewith the length
of the light path, has been changed. Consequently
the observer will see the thirty-first reappearance
of the moon not exactly thirty times 42J^ hours
after the first one, but earlier or later depending
on whether the earth and Jupiter have been ap
proaching or receding from each other. From
this information Romer ascertained the value of
31
TWENTIETH CENTURY PHYSICS
the velocity of light. Measurements on the velocity
of light with purely terrestrial tools did not become
possible until much later, when experimental tech
niques had reached a higher state of development.
Light travels 300,000 kilometers (186,000 miles)
per second; it could circle the equator almost eight
times in a second; but it reaches the earth about
eight minutes after leaving the sun, and requires
about four and one-half years to travel to the
earth from the nearest fixed star. It takes 100,000
years for light to traverse the milky way system
rectilinearly. And astronomers have knowledge of
systems related to the milky way, located far be
yond it, from which light travels 100 million years
before reaching us; thus we see these "nebulae"
as they were 100 million years ago.
The mere fact that light has the same velocity
of propagation as the electromagnetic waves pre
dicted by Maxwell would not have sufficed to justify
the proposition that light was a special case of elec
tromagnetic radiation. But light had already been
described as a wave radiation in Maxwell's times,
and more refined optical experiments (concerning
the "polarization" of light) indicated properties of
light which conformed exactly to the law of radia
tion mathematically constructed by Maxwell.
Spectral resolution of light and the synthesis
of white light from colored had already been ob
served by Newton in investigations which are no
less worthy of admiration than his celestial
mechanics.
But Newton did not consider light like sound
to be a wave motion. He preferred the interpre-
32
TWENTIETH CENTURY PHYSICS
tation that a luminous body, such as the sun, con
stantly emits hail showers of very tiny particles
and that this shower of light corpuscles is the basis
for what we perceive as light. Another explana
tion, already worked out by Huyghens in Newton's
time, was suggested by later research but was not
experimentally confirmed until afterwards, al
though Newton himself had described experiments
which could only be understood with the aid of
this new idea.
If we imagine two hail showers falling on the
same place simultaneously, or two machine guns
bombarding the same target, the result is neces
sarily an intensification, an addition of their effects.
In the case of light, however, there are cases where
light coming together with light produces darkness.
This phenomenon called "interference'' was in
vestigated in innumerable varied experiments ; upon
its practical application are dependent many of the
most important observation instruments of modern
physicists (e.g., spectroscopic "gratings"). The
existence of these interference phenomena becomes
understandable if one observes the intersection of
the circles (waves) produced on the water's sur
face by two stones thrown into it. The circles con
tinue through each other without being destroyed;
but where the wave crest of one and the wave
trough of the other come together, they annul each
other. That is the basis of the interference in
which two light excitations annul each other. These
interference phenomena as we see them show that
light is the result of a wave process. All interfer
ence effects ever observed, including their finest
33
TWENTIETH CENTURY PHYSICS
details, can be explained quantitatively by the con
ception of light as a wave motion, wherein, strictly
speaking, monochromatic light always corresponds
to a fixed wave length. Red light with a wave
length of about .00076 mm. and violet at about
.00038 mm. represent respectively the longest and
shortest wave lengths visible.
In this physical picture of light processes there
are no more colors; there are only oscillations in a
colorless electromagntic field. But we shall guard
against the careless methods of expression that
found favor in an earlier stage of natural scientific
development and philosophical adjustment. We
want to guard against a mode of expression such
as the following: now the "existence" of light is
disclosed and the coloration of light is recognized
as an illusion as something which originates in
our brain. As we know, no less a figure than
Goethe spoke out passionately against Newton's
theses on the color of light. It is beyond the scope
of this book to pursue any further the arguments
that Goethe used and the conceptions he developed.
But we shall consider his observations as a remind
er not to be too hasty in our judgments.
Certainly the establishment of the wave proper
ties of light has brought us no closer to the real
existence of blue or red, although refined experi
ments have taught us of the existence of remark
able new properties of blue and red light. Just as
when an object which has always been seen from
the front is viewed from the rear for the first
time; the new things that are learned are added to
what was already known; but it would be erroneous
34
TWENTIETH CENTURY PHYSICS
to say that through this consideration of the rear
side the "existence" of the entire object has been
recognized and its front side has been proven
an "illusion".
We shall still defer the questions which arise
here and which in general concern the most pro
found problems of physical knowledge and thought.
We shall still have sufficient opportunity to recon
sider the questions of natural scientific doctrines.
4. The Ether Problem. This discussion, in
striving to clarify the thought content of modern
physics and to make its philosophical conclusions
evident, is not bound to the historical sequence of
development. Our attempt to follow logical rela
tionships leads us along a zigzag path through
historical development.
Long before light was recognized (Maxwell) as
a special case of electromagnetic radiation, the
problem of how light waves could pass through a
vacuum had been pondered. Sound waves, in fact,
produce vibrations of the atmosphere and cease
to exist in the absence of air. But how can we
explain that light oscillations can take place also
in a vacuum? What oscillates here? To satisfy
these questions a new hypothesis filled empty space
with an obliging medium, fine, thin and all-pervad
ing the ether. Then the problem arose of infer
ring the nature of this ether from knowledge of
the laws of light phenomena and conversely, ex
plaining the laws of light by a mechanical model
of the ether.
When these questions arose at the beginning of
the last century the tools for their answers were
35
TWENTIETH CENTURY PHYSICS
already at hand in the highly developed mechanics
of that time. Based on the mechanics of centers of
mass, the basic concepts of which were described in
the first chapter, a mechanical theory of a material
medium which fills all space was set up* The
theory of elastic vibrations and waves in gases,
liquids and solids had essentially been established.
Here we must differentiate between longitudinal
and transverse waves; i.e., respectively between
those in which the matter oscillates parallel to the
direction of propagation and those in which the
vibration is perpendicular to this direction. Gase
ous media sustain only longitudinal waves, in which
case each minute volume of the medium is periodi
cally rarefied and compressed. Both types of waves
occur in solid bodies. Light waves had already
been proved through the aforementioned experi
ments on the polarization of light to be transverse,
never longitudinal. Thus if the ether is to be
considered as a material medium, it must be con
ceived of as a sort of solid body which opposes
any rarefaction or compression with infinitely great
resistance (possesses no "compressibility"). This
result was surprising in view of the fact that the
planets, as shown by experience, move on through
this ether without encountering the least resistance.
But if many other difficulties had not arisen this
fact alone would not have proved decisive. In any
case, not a single tangible new idea, not one sug
gestion for an experiment leading to new conclu
sions resulted from all the laborious experiments
on the mechanical ether model.
Maxwell's classification of light phenomena with-
36
TWENTIETH CENTURY PHYSICS
in the comprehensive framework of electromagnetic
processes produced a completely altered situation.
There resulted not only a knowledge of entirely
new relationships between light and other physical
phenomena and regularities but a changed spiritual
attitude toward these problems was facilitated.
Maxwell had succeeded in establishing the regu
larity of electromagnetic waves inclusive of light
with a completeness and mathematical clarity
which do not suffer by comparison to Newton's law
of gravitation. As Newton had, Maxwell could
say, "Hypotheses non fingo". Through Newton's
law all questions concerning the motion of planets,
moons, comets, etc., became answerable without
waiting for a possibly more thorough establishment
and explanation of this law. Similarly, through
Maxwell's law all questions falling within the re
gion of validity of his theory could be answered
precisely and independently of the problem of the
mechanical explanation of the properties of ether.
Maxwell himself did not follow the principle
"Hypotheses non fingo" absolutely; he had delib
erated over various extensions for obtaining a
mechanical ether theory. But the overall total
direction of his work pointed to something entirely
different. -It was the influence of his discoveries
which led more and more physicists to regard the
entire problem of the mechanical ether model as
fruitless and superfluous. For if it is possible to
predict the result of any conceivable electrodynamic
experiment, if electromagnetic processes can be
grasped as readily mathematically as the motions
in the planetary system then what more do we
want?
37
TWENTIETH CENTURY PHYSICS
Not only the method of thinking trained by
materialistic philosophy but also that physical in
stinct, which had learned from nature the more
profound significance of the physical "field of
force" laws as against the "action at a distance"
laws, resisted the recognition of Newton's (or
similar to this, Coulomb's) law as a non-derivable
physical elementary law. There remained only one
counter argument in which traditional materialistic
philosophy opposed Maxwell's theory, which already
depended on the idea of a "field of force" and had
clarified this idea with mathematical precision. This
philosophy maintained that only mechanical laws,
as evidenced in the pressure and collisions of atoms,
are to be recognized as the true and final laws of
nature, and that therefore only the reduction of
natural phenomena to a mechanical model can yield
a real "explanation", a real "understanding" and
a real "recognition" of the existence of things.
Since Maxwell's theory appeared as a mere de
scription of electromagnetic processes without really
attempting to explain their laws, it must have star
tled the advocates of the mechanical explanation
of nature when Kirchoff in 1876 began his lectures
on mechanics with the famous sentence, that it was
the function of mechanics "to describe the motions
proceeding in nature completely and in the simplest
manner." In that sentence he expressed a trend of
thought which had already been amply explained
and confirmed previously by Ernst Mach and which
is usually designated as physical "Positivism". 1
l lt should be noted that the spiritual scientific concept of
"Positivism" has no connection with the physical.
38
TWENTIETH CENTURY PHYSICS
This reference, which showed that the ultimate aim
of mechanics is simply a description of mechanical
events that it does not in any way lead us to any
"understanding" of the "essence" of mechanical
phenomena stripped the defense of the mechanical
meaning of the ether of its last weapon. When it
became evident that belief in a separate appreciation
of mechanical laws actually depends on habit only,
all inducement for considering the mechanical laws
as fundamental, like the Maxwellian electrodynam
ics, disappeared. The long since decided victory of
Maxwell's theory over the mechanical ether theory
conversely, modern physics traces mechanics back
to electrodynamics is therefore bound up with an
impressive displacement of the philosophical atti
tude of physical investigation. The new approach
can be characterized as a radical answer to the old.
It relinquishes just that which previously was con
sideredbe it in a vague sense or in the sense of
the materialistic philosophy as the true goal of
physical research; namely the penetration into the
heart of natural physical processes by stripping
them of all the cloaks of outer appearance. In
contrast we set a much more unassuming goal. We
recognize that we can achieve our final purpose
only by obtaining new data through experiments
and by winning support for the prediction of the
results of future experiments by a mathematical
description of the experimental determination de
veloped by the acuteness of theoreticians,
5. The Relativity Principle. The ether problem
is closely related to the relativity principle as it was
discussed in Chapter I. The existence of a lumin-
39
TWENTIETH CENTURY PHYSICS
iferous ether filling the empty interstellar space
would make it still possible to speak in a certain
sense of "absolute" motion; namely, motion relative
to the fixed ether. Then the statement that light
travels 300,000 kilometers per second would mean
that light moves forth with this velocity relative
to the fixed ether. In this case it must be possible
to determine an absolute motion through optical-
electromagnetic experiments, and we have already
seen that the detection of an absolute motion is
impossible through purely mechanical experiments.
This problem was thoroughly investigated ex
perimentally. The most famous example is the
experiment conducted by Michelson. He measured
the possible difference in light velocities on the
earth in mutually perpendicular directions with
very great accuracy; and the resultant difference
was exactly zero. 1 Obviously this experiment suf
fices to prove that there is nothing to be gained
from the primitive idea of a fixed ether permeating
interstellar space. All kinds of ways out were
attempted, for example, the hypothesis that the
ether surrounding the earth was carried along with
the earth in its motion. But such an idea leads
to very great difficulties. How far into interstellar
space does this zone of ether carried along by the
earth extend? How much ether does the sun carry
along with it?
Maxwell pointed out that if the notion of a
permanently fixed, space-filling ether were correct
the absolute motion of the solar system must be
detectable through observations on Jupiter's moons,
i Within the experimental error.
40
TWENTIETH CENTURY PHYSICS
in an extension of Romer's investigations. But
experience denies this, since the sun is really mov
ing relative to the fixed star heaven. Should it
therefore be assumed that as the earth carries along
its surrounding ether, the entire planetary system
also draws along a self -enveloping ether cloud?
Certainly the concept is becoming hopelessly com
plicated; and the many very accurate experiments
conducted along these lines must lead only to a maze
of most complicated results. That is not the case.
The Michelson experiment and a series of further
experiments which we shall touch on later in part
yielded conclusions which in themselves are very
simple and clear. The problem of developing an
incontrovertible, logical connection between the
varied (in themselves simple) experimental facts
requires rather deep penetration into the lowest
strata of our physical representation structure,
which had to be revolutionized and transformed
to agree with these facts.
"Aberration", a phenomenon discovered by Brad
ley in 1727, provided very simple, impressive coun
ter-evidence against the "carrying along theory".
If we stand on the front platform of a moving
train in vertically falling rain we get wet despite
the presence of roofing overhead. For the rain
drops falling perpendicular to the fixed earth (aside
from all the secondary influences of the air motion
produced by the moving train) are falling obliquely
relative to the train. An analogous phenomenon is
evident in the light of the stars falling on the
earth, which leads to the conclusion that in the
course of a year the fixed stars apparently execute
41
TWENTIETH CENTURY PHYSICS
small elliptical motions in the sky relative to the
earth's circular motion.
Finally, let us consider the Doppler effect. When
a whistling locomative is approaching us we hear
a higher tone than when it is receding from us
This is so because more sound waves sweep past
our ear per second as the whistle approaches than
when the locomotive is standing still or receding.
An analogous phenomenon manifests itself in the
case of light. From the displacements which the
spectral lines in the spectra of the fixed stars under
go due to this Doppler effect, both the earth's annual
motion and the motions of various fixed stars
towards and away from us can be inferred. In
the case of sound waves the magnitude of the Dop
pler effect is not only dependent on the relative
motion of the sound source and the listener, but
on the motion of both relative to the atmosphere.
Correspondingly, if there were a fixed ether, one
should be able to recognize absolute motions from
the optical Doppler effect. Actual experience shows
that this is not the case, that the optical Doppler
effect depends solely on relative motion and fur
nishes no possibility of determining an absolute
fixed ether. We can not summarize here the abun
dant detail of corresponding experimental facts
which bear out the relativity principle, not only in
mechanics, but in all branches of physics.
But even with this determination which deals
the ether representation a death blow we are still
far from understanding the problem; it is now
really posed for the first time. An attempt to de
scribe our complete optical-electromagnetic knowl-
42
TWENTIETH CENTURY PHYSICS
edge coherently in the all-inclusive form of the
principle of relativity encounters tremendous diffi
culties. To surmount these we must revise the
usual, apparently indispensable concepts which to
us are most self-evident. For though it is simple
to say that the relativity principle is also valid in
optics, we must accustom ourselves to the idea that
light always has the same velocity relative to any
moving body therefore, that the assertion "that
light travels 300,000 kilometers per second" not
only holds true for a particular condition of motion
of the observer but for all conditions of his uniform
rectilinear motion. But how can this "principle of
the invariance of the velocity of light" be estab
lished free from contradiction when elementary
thought habits assume that if we speed ahead in a
space ship at 40 kilometers per second behind a
light ray the velocity of the light ray relative to
us would appear diminished by the 40 kilometers
per second?
6. The Theory of Relativity. It required all the
acumen of the greatest physical thinkers of our
time to solve this puzzle. Modern publicity fre
quently supports the opinion that the so-called
"theory of relativity", in which these questions are
cleared up, is a quite personal, private discovery of
the famous physicist, Albert Einstein. Whereupon
they usually conclude that the challenging position
taken by the Third Reich toward Einstein person
ally with respect to political views must necessarily
result in a challenge of the theory of relativity.
This is a misunderstanding. It should be noted
that a number of other investigators also produced
43
TWENTIETH CENTURY PHYSICS
definite contributions to the theory of relativity
(Poincare, Lorentz, Minkowski, Planck, Hilbert,
Weyl, Eddington, etc.) and further, that the physi
cal knowledge expressed in the theory of relativity
would have been an inescapable logical conclusion
from the experimental facts if Einstein had never
lived. An attempt at a systematic explanation of
the theory of relativity would exceed the bounds
of this treatment. Just a few points are singled
out to help us examine the philosophical attitude of
modern physicists more thoroughly.
If we look out of the window of a train travel
ing 80 kilometers per hour at another train travel
ing in the opposite direction with the same velocity,
we can not determine our train's velocity relative to
the earth by seeing only the other train. The only
thing we can measure is our velocity relative to
the second train which relative velocity is obvi
ously 160 kilometers per hour. What is the basis
for our conviction that this is the case a convic
tion of which we are so certain that not a single
person will bother to actually determine it by meas
urement? We possess very deeply rooted thinking
habits that impel us to this opinion so forcefully
that we are wont to consider a divergent result as
merely logically foolish. As is known, Kant devel
oped the clever idea that our concept of nature is
conditioned essentially not through inherent qual
ities of the objects of nature but through changeless
thought patterns not derived from experience, but
incorporated by us into observations and investiga
tions of nature. He not only expressed these ideas
in a general form; but he also analyzed these ways
44
TWENTIETH CENTURY PHYSICS
of perception completely, attributing them invaria
bly to the nature of the human mind.
The physical experiences which lead to the
theory of relativity exhort us to a fundamental
distrust of constructions which denote certain ex
perimental data as independent and invariant. For
the theory of relativity teaches us to recognize that
a number of just such measurements are capable
of (and require!) modification and generalization.
Previously there existed the inclination to believe
in the certainty of their accuracy independently of
experimental experience. Let's take the above ex
ample of the two trains again: today we know
that the proposition that the velocity of the two
trains relative to each other is equal to the sum of
their (oppositely directed) velocities relative to the
earth is not really precisely correct. Actually this
relative velocity is a little smaller than the sum of
the two. In this example the difference is imper
ceptibly small; but, if instead of the railroad trains
we take two bodies which are moving with much
greater velocities quite a considerable t difference
results. If each of the two trains were traveling
at a speed of 200,000 kilometers per second (two-
thirds of the velocity of light) the relative velocity
would only amount to 276,923 kilometers per second
instead of 400,000. There is experimental evidence
to confirm this. The former opinion that appeared
certain without experiment was disproved by in
vestigation which confirmed it as practically correct
only under certain conditions (namely, only for
velocities that are much less than that of light).
This extension and change of ideas, that appeared
45
TWENTIETH CENTURY PHYSICS f
to us as invariably self-evident, and the develop
ment of new concepts, proven necessary by experi
mental experience, made possible the very great
usefulness of the theory of relativity.
In passing we noted the "positivist" attitude
toward the problem of physical knowledge merely
seeking a summarizing description of experimental
facts instead of an alleged explanation, penetrating
into the essence of things. This makes it necessary
to check most rigorously whether all our assertions,
suppositions and problems fit completely into a
system of pure description of observed results.
Any statement which falls beyond this limit espe
cially any attempt to express something about the
so-called "essence" of physical things must be
eliminated and declared basically meaningless. It
is overrating the significance and scope of physical
knowledge to believe it possible to make statements
that are not confined to a description of experi
mental measurements may these measurements be
confirmed, suspected, questioned or contradicted.
Modern developments have shown over and over
again with finality that only this radical liberation
of "senseless" opinions brought about by positivist
criticism gives scientific thought the necessary free
dom to adapt its ideas to the greater and more diffi
cult demands placed on it; demands due to the high
precision applied to the experiences of daily life
by modern experimental research and to the dis
closure of new, separate fields which lie completely
outside of our previous experience and thus com
pletely beyond the power of comprehension of our
customary, acquired modes of viewing. Concep-
46
TWENTIETH CENTURY PHYSICS
tions which appear most self-evident to us are fre
quently just the ones which prove to be the greatest
obstacles to the transformation of our ideas neces
sary to adapt them to the new experiences.
The theory of relativity includes one of the most
wonderful examples of the liberating force of this
positivist criticism on our opinions. What is meant
by the phrase, two events occur "simultaneously"?
No problem exists when both events take place in
spatial proximity, and can thus be seen in the same
glance. But what is meant by the assertion that
the falling of a stone on the earth occurs "simul
taneously" with an event on Sirius? The key to
the theory of relativity lies in the insight that, to
make any sense at all, the definition of the "simul
taneity" of two events widely separated in space
must be made concrete, must be transposed into an
experimentally verifiable form of expression. No
method but the following remains to effect this
definition. At the instant the stone falls on the
earth a light signal is emitted; at the same time
when the imagined event is taking place on Sirius
a light signal is sent out from there; and when the
earthly signal reaches Sirius, a light signal is sent
back from there at once. The reflected light signal
returns to the earth again about eighteen years
later. If the time elapsed between the earthly event
and the arrival of the first light signal from Sirius
amounts to nine years (more exactly, if it is just as
great as the separation between the times of arrival
of the first and second light signals from Sirius)
we say that the two events, on Sirius and the
earth, occurred "simultaneously",
47
TWENTIETH CENTURY PHYSICS
If signals existed that were propagated more
rapidly than light signals these would naturally be
used for the definition of simultaneity* If the
theory of "action at a distance" were correct the
difficulties of defining simultaneity would disappear
in general. For then it would be possible (in prin
ciple the question of the technical accomplishment
is an independent one) at the instant the stone fell
on the earth to dispatch a signal which would be
come perceptible on Sirius without any loss of time
at all perhaps through the Coulomb type of
"action at a distance". But we have accepted the
bases of the "field of force" theory, according to
which all physical effects require a finite time of
propagation an idea of decisive meaning for the
theory of relativity. By the "field of force" theory
the velocity of the signal can not exceed a definite
limit; and today we know that light possesses the
greatest signal velocity possible.
After the above definition for the notion of
simultaneity has been given, mathematical investi
gation leads to the perception of simultaneity as a
relative concept. Viewed from the abovementioned
train, which is traveling at 200,000 kilometers per
second, the two events on the earth and Sirius
would no longer take place simultaneously, since an
experimenter traveling in this rapidly moving train
would obtain a different result in executing the
measurements pertaining to the definition of simul
taneity than we would on the earth.
An example illustrates the remarkable results
which ensue. Consider a space ship traveling with
an enormous velocity almost equal to that of light.
48
TWENTIETH CENTURY PHYSICS
Suppose that the crew returns to the earth after a
one year voyage at a speed slightly less than that
of light. 1 Their watches, taken along in the space
ship, have measured just one year of time; their
one year stock of provisions has just been used up ;
and their hair has greyed just about as much as
would be expected from the hardships of a one-year
trip in interstellar space. But, arrived on the earth
the crew finds that in the meantime the human
race has aged one hundred years.
These are very remarkable assertions; and our
thinking which finds it too difficult to leave familiar
paths, is inclined, at first, to view them as pure
nonsense. But that is prejudiced. The sum of
these propositions forms a self-contained, incontro
vertible logical system; a system which does not
stem from the imagination, but is based on the
irrefutable facts of experimental experience*
Finally, it should also be mentioned that in con
nection with the theory of relativity in a general
ization of theory which extends far beyond what
we have discussed until now the problem of trac
ing Newton's gravitational attraction and "field of
force" laws back to fundamentals was solved. The
fact that the "gravity mass" of any body exactly
equals its "inertia mass" is conclusive for this solu
tion. Otherwise expressed, in ideal fall (in a vacu
um) all terrestrial bodies experience exactly the
same acceleration. Thus one can say that a physi
cist in a high elevator which is released and falls
down unhindered will make exactly the same obser
vations as another physicist who moved uniformly,
1 Namely, 0.05% less than the velocity of light.
49
TWENTIETH CENTURY PHYSICS
in a straight line through the universe in a space
ship in a region where the gravitational attractions
of the stars are ineffective because of their great
distance. To the physicist in the freely falling
elevator the weight of any body would be annulled;
and the physicist in the space ship, when his motion
was accelerated, would find the same effects in his
ship as the earthly gravitational field exerts. This
consideration leads to a more penetrating under
standing of Newtonian gravitation. We must deny
ourselves more exact treatment of this. One thing,
though, deserves emphasis in connection with these
considerations: the complete validity of Euclidian
geometry in actual physical space must be denied;
only approximate validity should be ascribed to it,
since more general geometric notions, which we
owe to the German mathematician Riemann, agree
more closely with real physical space (Einstein).
This also shows that we obstruct the path of physi
cal knowledge when we consider opinions and meth
ods of perception, which appear self-evident from
long familiarity, as irrefutable, invariable and inde
pendent of physical experience.
SO
CHAPTER III
THE REALITY OF ATOMS
1. Speculative Atomism. Actual proof of the
reality of atoms is an achievement of this century;
even at its beginning critical consideration required
the confession that atoms, although investigators
spoke of them, were still no more than a stimulating
and useful hypothesis, which in the final analysis
was unproved and possibly unnecessary, perhaps
even misleading. Although the idea of atomism
was important and fruitful at the very beginning
of western natural research, this idea did not
originate from western research itself; just as we
borrowed the model for mathematical thinking
from the Greeks, we took the atomistic interpreta
tion of nature from them.
Nothing exists Democritus taught except
atoms and vacuum; everything else is imagination.
These innumerable atoms, indestructible and invari
able elementary constituents, are to be considered
the basis for all beings and events in nature. Indi
vidual atoms possess invariable geometric form and
motions which fluctuate due to the pressure of and
collision with other atoms. In all changes in the
structure of nature the atoms are always preserved;
from hothing comes nothing; nothing which exists
can be destroyed; change is merely combination
and separation of parts. The differences f all
things stem from the diversity of their atoms in
number, magnitude, structure and arrangement
51
TWENTIETH CENTURY PHYSICS
Since the movements of each individual atom are
regulated according to natural law, nothing arbi
trary can happen in all nature; nothing happens
accidentally, but everything from a cause and of
necessity. Our rough senses can not recognize
these amazingly fine elements in their true nature
and form, but experience their effects only vaguely.
"Only in the imagination does sweetness exist, in
the imagination bitterness, in the imagination heat,
cold, colors; in reality nothing exists but atoms
and vacuum."
This is marked evidence of that "decoloration"
of the world, the assurance that all direct sensory
observation is an illusion and that a knowledge of
the true status of things must lead us to a picture
in which nothing remains but the geometrical form
and mechanical motion of the atoms. These idea
forms of materialistic philosophy introduce the pos
sibility of considering all events in nature as results
of strict regularity; the gist of the basic concept
of natural scientific thought is anticipated here in
general and is thoroughly formed for the first time.
On the other hand we must not forget to recognize
how radically this philosophy opposes religious
representations of its time. For the Greeks every
stream was a God; in the springs lived the nymphs,
in the woods the horned Pan, and in caves and
caverns resided demons. This entire mythological
picture of the world, which suspected the arbitrary
and incalculable influence of demoniacal powers
in every natural process, was pushed aside by the
powerful conception of a picture of nature of
stricter regularity, Epicurus, who renewed Demo-
52
TWENTIETH CENTURY PHYSICS
critus* teaching, and who in his thinking and con
duct of life combined a rationalistic, vigorous atti
tude with a very cultivated, fine-spirited being, was
not so brutal as to deny existence completely to the
Gods. He let them continue as blessed, immortal
beings, occupied with themselves, and never infring
ing upon the workings of the world these work
ings being developed according to the mechanical
lawfulness of atomic motions in strict, definite
sequence. In a great didactic poem "De rerum
natura" the Roman Lucretius explained completely
the ideas of atomistic regularity for all the fields
of nature known at that time. These teachings
were made known to western scholars in connection
with the humanistic studies of the Renaissance;
Gassendi, principally, introduced Greek philosophy
into western science.
Let us consider the ideas which Newton, together
with Gassendi, applying the divergent theories of
Descartes, formed about the construction of matter.
F. Dannemann explains them as follows in his his
torical work 1 on the natural sciences: "He consid
ered it most plausible, that it (matter) consists of
solid, impermeable, moving particles. Since natural
bodies, e.g., water, are invariable in their properties,
the particles of which they consist must neither be
able to be used up nor destroyed. The variation of
material things is to be laid exclusively to the
separations, combinations and movements of those
invariable particles." These are, as is obvious,
exactly the concepts of materialistic philosophy,,
1 The Development and Inter-relation of the Natural Sci
ences. Four volumes. Leipzig 1910-1913.
S3
TWENTIETH CENTURY PHYSICS
almost unchanged, just as Democritus stated them.
But Newton was outside of natural science in
no wise an adherent of materialistic theories. For
him these ideas meant nothing but a clue to physical
research; he did not see in them the support of
radical, world-viewing results.
2. The Natural Scientific Evaluation of the
Atomic Concept. Dalton first recognized and effec
tively utilized the stimulating force of the atomic
concept and its ability to guide future physical
research. To him we owe the use of the idea of
atoms for understanding basic regularities of chem
istry. Chemistry makes a sharp distinction between
mixtures of different substances and chemical com
binations. A mixture as, for example, a solution
of sugar in water or a mixture of nitrogen and
oxygen can include arbitrary (within certain
limits) relative proportions of the constituents. In
a nitrogen-oxygen mixture the portion of oxygen
can be varied continuously by addition or removal ;
correspondingly, the mixture exhibits properties
somewhere between those of pure oxygen and of
pure nitrogen, depending upon the relative concen
tration. Also, the mixture can be separated into
its constituents through relatively superficial means.
In a chemical combination entirely new properties
appear, which can be quite dissimilar to those of
the constituents. The proportions of the compon
ents of a chemical compound are quite stable and
cannot be varied continuously. Thus exactly 16
grams of oxygen always combine with 2.016 grams
of hydrogen to form water. Another chemical
substance, hydrogen peroxide, can be formed from
54
TWENTIETH CENTURY PHYSICS
2.016 grams of hydrogen and just 32 grams of
oxygen. It is striking that exactly twice as much
oxygen is utilized in the second case as in the first;
and on the basis of the atomic concept Dalton found
a clear explanation for such facts, which occur
similarly in all chemical combinations. His explan
ation was as follows: The "molecule" of water,
i.e., the smallest possible particle of water, contains
only one atom of oxygen; the molecule of hydrogen
peroxide however contains two atoms of oxygen,
while it contains just as many (two) atoms of
hydrogen as the water molecule. Here we arrive
at the distinction between atoms and molecules;
we designate the smallest particles of chemical
compounds as molecules, which for their part con-
gist of atoms of the chemical elements. According
to Dalton's ways of thinking a comprehensive study
of proportions by weight in chemical compounds
rendered the determination of the relative atomic
weights of all the elements possible. The "atomic"
weight of oxygen is arbitrarily designated by the
value 16, whereupon hydrogen acquires the atomic
weight 1.008 and every other element, similarly,
receives a definite atomic weight derived from
chemical weight relationships.
The regularities which the gases exhibit, which
in the case of sufficiently small densities assume an
"ideal" form, proved very helpful for the clarifica
tion of these ideas; for example, in the sense that
a gas mass contracts to one-half its original volume
when, with constant temperature, the pressure im
pressed upon it is doubled. Criteria existed for
the hypothesis that not only in compounds but also
55
TWENTIETH CENTURY PHYSICS
in a gaseous element such as nitrogen the particles
moving at random through space are not necessarily
identical with atoms ; in nitrogen, for example, each
"molecule" of the gas consists of two atoms. In
the chemical combination of gases (with constant
pressure and temperature) there is a simple relation
between proportions by weight and volume relations
(proportions by volume) between the chemical com
pound and the still uncombined constituents. To
fit these facts Avogadro introduced the explanation
that equal volumes of all gases measured at con
stant pressure and temperature always contain the
same number of molecules. Based on this "Avoga-
dro's principle" a "molecular weight" can be deter
mined for each gas independent of chemical weight
relations. The molecular weight of a chemically
homogeneous gas is equal to the mass of 22.4 liters
of this gas measured in grams at one atmosphere
of pressure and a temperature of C. Experi
ence shows that values obtained in this way corre
spond with the chemically defined atomic weights.
In many elements, e.g., the metals, this molecular
weight is exactly the same as the atomic weight;
thus metallic vapors are "monatomic". In the afore
mentioned nitrogen, however, the molecular weight
is exactly double the atomic weight. And in water
it equals 18.016 (2 X 1.008 + 16) in accordance
with its above-described chemical composition.
These ideas are further verified by simple relations
of molecular weights such as "diffusion velocities",
or by the characteristic difference between the
specific heats of "monatomic" and "polyatomic"
gases. None of these, it must be emphasized, are
56
TWENTIETH CENTURY PHYSICS
proofs for the correctness of the atomic concept;
but they are proofs for its usefulness. The atomic
idea describes very plainly a large number of im
portant and comprehensive regularities, thus facili
tating greatly our progress with these phenomena.
Crystallography furnishes evidence of further
regularities which are certainly clearly explained
by the atomic idea, though they too do not lead to
proofs for the reality of the atom. In the crystal
line state of matter the atomic concept suggests a
regular grouping of the atoms or molecules, along
side of each other and arranged in layers. This
view induces important results; on this basis the
variety of possible forms of crystals are shown
mathematically to be limited very considerably. The
completion of this mathematical proposition yields
the wonderful result that according to the atomic
concept there should be no more nor less than 32
different "crystal classes" which are defined by
different properties of symmetry. Actually this
confirms precisely the experience of mineralogists;
there really occur in nature all the crystal forms
(crystal symmetries) which are compatible with
the atom idea, but not one single one which contra
dicts it. The so-called "law of rational indices"
discovered by the mineralogists formed an impor
tant adjunct to this original consideration, which
is related only to the symmetry properties of differ
ent crystal forms. . If we imagine the crystal as
built up of a regular stratification of layers of
atoms, then its outer boundary surfaces could never
lie so that they partially cut through the atoms.
The limits for the possible positions of the bound-
57
TWENTIETH CENTURY PHYSICS
ary surfaces given by this view are exactly equiva
lent to the requirements which the law of rational
indices places on the position of the crystal surfaces.
Such experiences must necessarily encourage the
more and more energetic pursuit of the atomistic
notion which intrinsically was so clear even
though tangible proof for the reality of atoms was
still lacking. Actually the theoretical development
of the atomic concept was furthered extensively
by the most able physicists. We have already
mentioned ideal gases and indicated how the gas
eous state of aggregation should be represented on
the basis of the atomic theory; the molecules of a
gas are completely separate from each other; each
one moves along with high velocity until it meets
another one, and then, in elastic rebound, their
direction of motion and speed change. The con
tinuous impact of countless molecules on the walls
of the enclosing vessel produces the pressure of
the gas, perceptible to us with our rough tools.
These ideas were elaborated thoroughly (Clausius,
Maxwell) and our understanding of the gaseous
state of aggregation was developed very clearly
and completely. Whereby the proof resulted that
Avogadro's principle, first only speculatively sus
pected, must necessarily be correct if the atomic
hypothesis proves at all valid.
The discovery of the energy principle (Mayer,
Joule) further strengthened confidence in atom
ism. It was recognized that mechanical energy,
which disappears through friction or the like, re
appears in the quantity of heat produced in such
a way that a definite amount of consumed me-
58
TWENTIETH CENTURY PHYSICS
chanical energy corresponds to a definite number
of calories of heat. Conversely, according to the
same conversion relation, in steam engines quanti
ties of heat are transformed again into mechani
cal kinetic energy. This conversion of mechanical
energy into heat and its converse can be con
sidered quite consistent, in the sense of "macro-
physics". Whereupon one must establish that
energy, which has proved indestructible, can as
sume both the form of a quantity of heat and of
mechanical energy. The "macrophysical", "pheno-
menologic" heat theory thus arrived at is entirely
sufficient for answering all the questions encoun
tered in connection with heat engines, and with
heat conversion in chemical processes.
But further thought is suggested to give the
process of the conversion of mechanical energy
into heat a clear interpretation in the light of the
atomic theory. In a gas, as was represented above,
the concepts of heat and temperature are not ap
plicable to the individual molecules, but only to
the gas mass as a whole. In an individual mole
cule only the kinetic energy, i.e., its velocity
of motion, or at best also its rotation, can
be changed. Thus, if energy is added to- a gas
mass, which appears macrophysically as added heat,
it can only mean that the average energy of motion
of the gas molecules has increased. The exact
determination of the connection between the aver
age energy of motion of the gas molecules and the
temperature of the gas is a part of the theoretical
investigations on the "kinetic theory of gases",
which. has already been discussed.
59
TWENTIETH CENTURY PHYSICS
Similarly, in a solid body, a crystal perhaps, the
temperature and heat energy contained within it
are conceived of as mechanical energy of its mole
cules or atoms. Although in their regular arrange
ment in layers no one atom can leave its place, fine
vibrating motions within the crystal possibly sim
ilar to the fine vibration of a heavily traveled steel
bridge are still possible. If these vibrations with
in the crystal are so small that they are not percep
tible to us as mechanical motion, we do note the
energy of these motions as heat content which
manifests itself in the temperature of the body.
(If the atoms contained in each small piece of the
crystal move by very small amounts in random
directions, the whole crystal appears motionless to
our macrophysical senses.)
Apropos of such thought processes was Boltz-
mann's atomistic interpretation of a remarkable
regularity in heat phenomena. If we imagine that
a planet's motion is interrupted and the planet then
is induced to move in the opposite direction with
the same velocity, it will retrace its entire elliptical
path in the opposite direction after the reversal.
This is an example of the fact that all purely
mechanical motions are, as we say, reversible. The
upward motion of a stone, thrown from the earth,
(in the ideal case) until its point of reversal is an
exact temporal mirror image of the subsequent
downward motion. Similar reversibility which
can also be denoted as a physical "symmetry of the
positive and negative time orientation" exists in
all purely electromagnetic properties.
But when we move a body over a table surface
60
TWENTIETH CENTURY PHYSICS
against frictional forces and heat is generated
thereby, there is no reason to expect that in moving
the body backwards along the same line the con
verse is true that the heat energy will change back
to energy of mechanical motion. Or take an elec
tric current which flows through a wire and pro
duces heat when it flows through the wire in the
opposite direction it again produces heat; the heat
energy does not change back into electrical. These
are examples of irreversible processes. Another
example of such a process is the mixing of two
liquids ; in most cases these intermix by themselves,
but this process never runs backward of itself. A
further example of importance to us is the follow
ing: if a gas filled vessel is introduced into an
evacuated one and is opened there, the gas diffuses
throughout the entire available volume. It is not
impossible to restore the original conditions; the
larger vessel can be evacuated again by pumping
and the gas can be compressed into the smaller
one. But this does not constitute an exact reversal
a temporal reflected image of the first process;
and it can be considered that for the restoration of
original conditions after any irreversible process
a definite "compensation" must be included (Clau-
sius). In the steam engine, which undertakes to
convert quantities of heat into mechanical energy,
there does not occur a simple reversal of the process
of the production of heat through friction, but each
steam engine functions according to a scheme simi
lar to the following: a certain amount of heat is
removed from a heat container maintained at a high
temperature. A fraction of this amount is changed
61
TWENTIETH CENTURY PHYSICS
into mechanical work, while the remainder is con
ducted into a heat reservoir of lower temperature.
As "compensation", therefore, for the conversion
of heat into work there occurs the transfer of a
quantity of heat from a hotter body to a colder
one i.e., therefore a process which nature could
perform "irreversibly" itself, since in heat conduc
tion the heat always flows from higher to lower
temperature.
The occurrence of such "irreversible" processes
among heat phenomena posed a very difficult prob
lem for the "kinetic theory of heat" tracing back
the laws of heat to the mechanics of atoms. For
purely mechanical processes were shown to be
always reversible, which makes it appear impossible
to trace these irreversible heat phenomena back to
mechanical properties. The solution of this diffi
culty, achieved through Boltzmann's perspicacity,
runs as follows : in an aggregation of many similar
particles, such as are attributed to every physical
system by the atomic theory, there is no point to
pursuing the motion of each individual atom or
molecule; it is only important to us to observe the
average statistical behavior of large numbers of
atoms. Thus statistical concepts are necessarily
introduced into the consideration and we must de
termine which (defined in a rough statistical sense)
events are to be considered as especially probable
(thus as occurring very frequently) in comparison
with other conceivable processes.
For our example this signifies that when the
small gas filled vessel is opened in the large empty
one "it is extremely probable" that the gas will
62
TWENTIETH CENTURY PHYSICS
stream out and distribute itself uniformly in the
large vessel. Strictly speaking it cannot be defin
itely known that this will happen; indeed, to view
the processes of motion in the gas mass with the
same complete certainty achieved for planetary
motions one must know quite exactly the position
and velocity of each individual molecule at the
beginning of the experiment. The fact that, in
stead of this, we simply denoted the initial condition
of the experiment statistically stipulates that we
can not predict its further progress with complete
certainty, but only with very great probability.
The reversibility of pure physical processes,
which according to the atomistic conception is the
basis for macrophysical heat phenomena, depends
upon the existence of an exact reversal, an exact
temporal reflected image for every process where
by it can happen that the gas mass distributed in
the abovementioned large vessel contracts into the
smaller one, in an exact reversal of the normal
process. No one can guarantee that this is com
pletely out of the question; but we can show that
such an event is extremely improbable mathe
matically its probability is expressed by an infini-
tesimally small number. Thus it becomes clear that
despite the fundamental reversibility of atomistic
elementary-processes, yet, on a large scale, in macro-
physical events, practically irreversible phenomena
take place.
Another instructive example of an irreversible
process is the mixing of two gases or liquids with
each other. According to the kinetic-atomic theory
this problem is somewhat similar to the one wherein
63
TWENTIETH CENTURY PHYSICS
two types of balls red and white ones for instance
are thoroughly shaken up in a sack. If the red
and white spheres are carefully separated initially,
they will become completely mixed up after further
agitation. If, then, we continue to shake, it is pos
sible in principle that the original separation of red
and white balls will be restored but practically
this possibility is of little moment since it would
require shaking for astronomically long periods of
time before this "spontaneous separation" could be
expected with appreciable probability.
A quantitative measure for the irreversibility of
a thermodynamic process (from a purely macro-
physical standpoint) can be specified in the form
of "entropy" a quantity which always increases
to a maximum in irreversible processes and does
not decrease again (Clausius). According to Boltz-
mann this entropy can now be defined through the
atomic concept as a measure of the disorder in an
atomic aggregate. As the above example of the
mixture illustrates, in an incompletely "disordered"
system, the probability of further disorder is ex
tremely great.
3. The Limits of the Divisibility of Matter.
Everyday experience, which appears to show un
limited divisibility of matter, through simple re
finements makes it certain that atoms must be ex
traordinarily small, and that therefore the number
of atoms in a gram of any substance must be enor
mously large. For an exact measure of this quan
tity we use the so-called Loschmidt number. As a
"gram-atomic weight" of an element we denote a
mass of a number of grams equal to the atomic
64
TWENTIETH CENTURY PHYSICS
weight; the Loschmidt number is the (equal for
all elements) number of atoms in a gram-atomic
weight. Evidence for the divisibility of matter
can be obtained by distributing a minute amount
of a strong-scented substance (mercaptan) in a
large quantity of air and then determining to what
degree of dilution, the odor can still be perceived;
or by dissolving a strongly colored liquid (eosin)
in a relatively large quantity of water and then
noticing to what degree of dilution a uniform color
ation of the water remains perceptible. A still
more suitable experiment involves the use of a very
dilute solution of fluorescein, a substance which
fluoresces strongly in incident light. Extremely
small volumes of the solution are examined with a
microscope to determine to what degree of dilution
a spatially uniform fluorescence can be detected.
From such observations it can be inferred (Perrin)
that the Loschmidt number is definitely greater
than 10 21 (a 1 with 21 zeros after it).
But quite simple, daily experiences occur that
indicate the limits which its atomistic structure
places on the subdivision of matter. These involve
utilization of very thin membranes of matter. Gold
leaf, which is used for gilding purposes, is ham
mered down to an exceptional thinness when held
against the light it exhibits a greenish translucence
of about 100 millimicrons (a million millimicrons
make a millimeter) ; and yet this thickness is still
far removed from the ultimate limit. But there
exist direct indications for the atomistic constitu
tion of matter in commonplace, familiar soap bub
bles, often formed when washing by a film of soapy
65
TWENTIETH CENTURY PHYSICS
water stretched between the thumb and index
finger. These bubbles iridesce in variegated colors,
whose diversity and rapid shifting is evidence of
the variations in the thickness of the bubble with
position and time. Small dark spots appear in a
thus colored bubble, which at first may be consid
ered as holes, but which in reality are enclosed by
still thinner soap films. If bubbles like this are
produced in a solid frame instead of in the hand,
and if they are protected from evaporation in a
vapor-filled enclosure, they can be preserved for
days. Newton had disclosed that inside these black
spots i.e., this membrane which weakly reflects
light still blacker, thus still thinner membranes
are formed. The thickness of the thinnest mem
brane obtained by Newton was about 6 millimi
crons, about 20 times thinner than gold leaf. But
the next thicker membrane obtainable, just before
this thinnest one, is of exactly double thickness.
This provided a tangible indication of the molecular
structure of this skin substance; obviously, the
thinnest membrane represents a single layer of
molecules, while in the next thinnest one two layers
are piled together. A very thin film can be pro
duced more conveniently by allowing a minute
amount of oil to spread out on a large water sur
face. The familiar iridescent films which oil forms
on water correspond in their thickness approxi
mately to the usual soap bubble. Much thinner oil
films which are no longer directly visible but can
be recognized with simple tools can easily be
formed. In these thicknesses of about 1 millimi
cron have been reached; and in these it has again
66
TWENTIETH CENTURY PHYSICS
been shown that the thicknesses of the finest films
are not continuously variable. As in the soap
bubbles, we find a quite definite thickness prescribed
for the thinnest, second thinnest, etc. oil film (for
a definite previously determined type of oil). The
limits of the divisibility of matter have actually
been reached here.
Further highly informative investigations were
performed on very small corpuscular particles.
Here the invention of the ultra-microscope ren
dered important service; it made visible not only
the form, but also the position and motion of
particles which cannot be "seen" in the usual sense,
since there are limits, defined by the nature of light,
for the optical observation of very small objects.
Bodies of dimensions smaller than the wavelength
of visible light cannot be "formed" in any way by
light rays; cannot be made visible in their true
form. The ultra-microscope, through an ingenious
device, made it possible to detect optically the
presence of particles which are somewhat smaller
than the wavelength of visible light.
For the fundamental task to prove the reality
of atoms experimentally two types of investiga
tions in particular have rendered real contributions.
If very small particles are placed in a liquid it
appears that they do not sink rectilinearly to the
bottom and remain there but rather they move
through the liquid in an irregular, erratic manner.
The motion becomes more intense the higher the
temperature of the liquid is raised; but it is inde
pendent of a minor agitation of the enclosing vessel
or of other accidental disturbances. Also, if left
67
TWENTIETH CENTURY PHYSICS
undisturbed, the erratic motion ,of the particles con
tinues for days or years. This Brownian movement
serves as a direct proof for the correctness of the
proposition, set up by the atomic theory, that the
heat content of a body is to be conceived of as an
internal motion which is so fine that it cannot be
macrophysically detected as such. One must not
conclude that there are very fine motions or cur
rents in the liquid which produce the Brownian
movement of the suspended particles. That would
lead to the idea that the motions of a throng of
closely neighboring particles were somewhat similar
as is the case with dust we see around us in the
sun's rays. In Brownian movements two approach
ing particles in a liquid are completely independent
of each other, and thus separate again very soon.
This shows that the hidden motions in the liquid,
the permanent presence of which must be regarded
as characteristic of the heat condition of the liquid,
are completely "irregular" and macrophysically
absolutely imperceptible.
Brownian movements have become the subject
of many experimental investigations, for theoreti
cal considerations had shown (Smoluchowski, Ein
stein) that its precise observation permits definite
conclusions about the motions of atoms and mole
cules, through irregular collisions with which the
particles in Brownian movements are driven
around. It was possible to infer from investigation
of Brownian movements how great the average
kinetic energy of the individual molecules must be.
And since the total heat energy contained in the
liquid is equal to the sum of the energies of the
68
TWENTIETH CENTURY PHYSICS
individual molecules, we can infer how many mole
cules there are in a given volume. This leads to a
determination of Loschmidt's number.
Related investigations and considerations are also
feasible in many kinds of "fluctuation phenomena".
Imagine an armor plate suspended from chains
and blown upon by a very strong, uniformly oper
ating sand blast apparatus ; the plate will be forced
from its equilibrium position by the pressure of the
blast and will then hang in a slightly different posi
tion. Now, we remove the sand blast apparatus
and by bombarding the plate with machine guns
exert the same total pressure on the middle of the
plate; the armor, struck over and over again by
the single shots again assumes the displaced equi
librium position, this time continuously oscillating
irregularly about this equilibrium position. Ob
serving just these oscillations, one can determine
the strength of the single blows striking the plate.
Similarly in many types of physical apparatus very
fine irregular fluctuations can be observed and from
them the magnitude of the Loschmidt number can
be determined. In the very fine physical apparatus
the presence of the irregular heat motion of the
atoms can be detected; thereby most varied meth
ods can be utilized for determining Loschmidt's
number. The values of Loschmidt's number ob
tained from all such investigations have always-
agreed within the limits of their accuracy.
The following describes the second possible way
of determining Loschmidt's number from investi
gations on very small particles: the density of
the earth's atmosphere decreases, as we know, with
69
TWENTIETH CENTURY PHYSICS
increasing height. Imagine two very high cylin
dersabout 100 kilometers high to be filled re
spectively with two different gases, perhaps oxygen
and nitrogen. It is demonstrated that in the gas
whose molecules are heavier (oxygen) the density
decreases outward from the earth's surface more
rapidly than in the other gas. .The gas molecules
are hindered by their kinetic energy from simply
accumulating on the bottom of the vessel, i.e., form
ing a liquid. But the heavier they are, the stronger
is the effect of gravity forcing them downwards
and thus the more rapidly does the gas density de
crease with increasing height above the earth's
surface. The mathematical law relating to this
states that the comparison of the decrease in density
in the two cylinders depends solely on their mole
cular weights.
This was most useful in its application to the
production of an artificial gas in which the actual
mass of the individual molecules is known. Perrin
laboriously produced large quantities of small resin
pellets of equal weight. He obtained these resin
particles from an emulsion which originally con
tained particles of the most varied magnitudes ; but
by an ingenious procedure, involving painstaking
work, he was able to separate out particles of cor
responding mass whose diameter was from 200 to
300 millimicrons. These particles were then placed
in water. (We know that with sufficient degree
of dilution dissolved substances, e.g., sugar in
water, behave analogously to the ideal gases.)
Thus, the resin particles placed in the water repre
sented an ideal gas and vessels a kilometer high
70
TWENTIETH CENTURY PHYSICS
were no longer needed to determine the decrease in
density with increasing height with this artificial
gas; even in small containers these artificial gas
molecules, enormously heavy in comparison with
usual molecules, crowd together noticeably at the
bottom. Through measurement of this effect and
comparison with the known decrease of atmo
spheric density with increasing altitude it is possible
to compare the directly determined mass of these
artificial, huge molecules with the masses, absolute
values still unknown, of the chemical molecules
present in the atmosphere. Thus a new approach
to the weighing of molecules or differently ex
pressed, to a determination of Loschmidt's number
is reached.
The numerical value which resulted from these
different determinations of Loschmidfs number
(and from further determinations still to be dis
cussed) is 6 x 10 28 (a 6 with 23 zeros after it).
If the hydrogen atoms contained in 100 grams of
water were distributed over the entire earth's sur
face, one atom would fall on each square centimeter.
4. The Conclusive Proof. Finally we come to
the experiments in which single atoms are actually
isloated and made, in a manner of speaking, tangi
ble, so that there is no longer any possible doubt
concerning their real existence.
Let us begin with Laue's famous discovery of
crystal interference. Modern workers in physical
optics and spectroscopy no longer fcse only prisms
for the spectral resolution of light; the diffraction
grating has become much more important. When
numerous lines at equal, close intervals are scribed
71
TWENTIETH CENTURY PHYSICS
upon a polished surface, a monochromatic (includ
ing just one wave length) light ray will neither be
reflected from this surface as from a usual mirror
nor as from a rough surface which reflects diffuse
ly toward all sides. The ray is reflected in a series
of definite directions which vary according to its
wave length; in all other directions there is no
reflection because the light excitations traveling in
these other directions mutually annul each other by
interference. This knowledge (a special interfer
ence experiment) gives us, as previously mentioned,
the clearest and most obvious proof for the wave
character of light and makes it possible to deter
mine the wave length of the light just from a
knowledge of the spacing of the grating lines. (In
common gratings this is between a hundredth and
a thousandth of a millimeter.) Conversely natur
ally the separation of the rulings on the grating, if
by chance this value is not known, can be deter
mined from the reflection produced by this grating
with light of known wave length.
X-rays, on traversing crystals, exhibit remark
able interference effects which are related to those
of the "line grating" described but are consider
ably more complicated. The discovery of these
effects proved two things with one stroke; first,
that X-rays are a wave radiation; and second, that
crystals possess a fine grating-like structure, which
is so fine that it defied observation with former
tools. Careful analysis of the varied and compli
cated interference phenomena which can be obtained
in this way led to the certainty that this internal
fine structure of crystals is exactly the same as that
72
.TWENTIETH CENTURY PHYSICS
which atomistic concepts led us to expect; the
"illumination" of crystals with X-rays clearly
displays their synthesis from atoms and thereby
conclusively assures the reality of these atoms.
The wave lengths of X-rays are much shorter
than those of ordinary light (X-rays, like light,
are also included within the general bounds of the
classification of Maxwell-Hertz electromagnetic
waves). Because of their short wave lengths it is
not possible without further refinement to attain
diffraction (interference) of X-rays with the usual,
relatively rough optical line gratings. But in crys
tals nature presented us with "natural diffraction
gratings" with which we can study X-ray inter
ference effects. With a very refined device it was
possible to obtain diffraction of X-rays with an
optical diffraction grating (line grating) so that
the wave lengths of X-rays could be measured just
as optical wave lengths are. If we know the wave
length of an X-ray, from the interference effects
which result from the passage of this X-ray
through a crystal we can infer the volume relations
within the crystal. X-ray interference effects in
crystals not only substantiate the reality of atoms
with indubitable clearness and distinctness, but
also facilitate another determination of the number
of atoms in a macroscopic piece of matter a new
determination of Loschmidt's number.
Millikan (in extending and refining older, less
lucid ones) performed an experiment which was
striking in the simplicity of its fundamental idea.
In it he provided tangible proof for the atomic
nature of electricity. A mist of minute oil drop-
73
TWENTIETH CENTURY PHYSICS
lets is sprayed into a chamber; many of these are
electrically charged in the process of their produc
tion. One droplet is singled out and observed
through a microscope. Left to itself it falls verti
cally downward, due to the force of gravity; not
according to the ideal laws of free fall, but rather
with constant velocity, since air resistance is pro
portionately more effective against these small
droplets than against larger bodies. If the droplet
is subjected to the influence of an electric field, of
proper intensity perpendicular to its direction of
fall and opposing it, the droplet will start to rise,
with a constant velocity, the magnitude of which
is dependent upon the field strength. The ratio of
the forces working in both cases and the magnitude
of the charge carried by the droplet can be calcu
lated from a comparison of the speeds of rising
and falling. Consideration of the values obtained
for numerous such droplets indicates that the mag
nitude of the charge does not vary continuously
from case to case; none of them ever has a smaller
charge than the so-called "elementary charge", and
larger values are integral multiples (2, 3, 4 . . .) of
this smallest one. Thus we have tangible evidence
that electric charges cannot be artibitrarily divided
indefinitely; rather, all electric charges are com
posed of indivisible "elementary charges", each of
which carries a charge of 4.77 x 10~ 10 (4.77 divided
by a 1 with 10 zeros after it) electrostatic units. 1
1 The electrostatic unit of charge (e.s.u.) is that charge
which, placed 1 cm away from an equal, like charge (if both
charges are considered concentrated in the form of points)
exerts upon it a repulsion (force) which will impart to one
gram (unit mass) an acceleration of 1 cm per sec 2 (unit
acceleration).
74
TWENTIETH CENTURY PHYSICS
This atomism of electricity is closely related to
the atomism of matter in general. A law concern
ing electrolysis, discovered by Faraday and named
after him, states this relation. Helmholtz had
early concluded from this law that if the concept
of the atomism of matter were proven correct an
atomism of electricty must be assumed. If one zinc
and one copper plate are immersed in an aqueous
solution of copper sulf ate and an electric current is
passed through the solution in a positive direction
from the zinc to the copper plate, the zinc gradually
becomes dissolved in the liquid as further copper
is deposited on the copper plate. Quantitatively
this experiment shows that when one gram atomic
weight of zinc has been dissolved, just one gram
atomic weight of copper has been deposited; and
corresponding weight relations are found to hold
for all similar electrolytic experiments. Moreover,
the number of gram atomic weights deposited or
dissolved always remains in a simple proportion
to the quantity of electric charge which has passed.
Thus there occur here regularities of the same
character as the laws of weight relations in chem
ical reactions which Dalton explained by the con
cept of atomism. In these laws Dalton saw a cri
terion for the definition and use of the atomic
concept; by the same right we can, with Helm
holtz, infer the atomistic structure of electricity
on the basis of Faraday's law.
Conversely, knowing from Millikan's work that
the atomism of electricity not only expresses an
auxiliary idea but is a real fact, we can infer from
Faraday's law that the atomic structure of matter
75
TWENTIETH CENTURY PHYSICS
is a reality (which has already been verified in
our consideration of crystal interference). The
knowledge of the magnitude of the elementary
electric charges furnishes one more basis for calcu
lation of Loschmidt's number, characteristic of
this atomistic structure of matter.
This in no way exhausts the experiments which
show the indubitable reality of atoms. Further
direct proofs for atomism are gained in connection
with the investigation of radioactivity. From the
observation of radioactive preparations it was de
termined that "alpha-radiation" is simply an emis
sion of electrically charged helium. When this
alpha-radiation strikes a suitably prepared zinc sul-
fide screen, even with limited intensity, it produces
a series of small light flashes (scintillations) there.
From this effect it is seen that the emitted electri
cally charged helium is not an arbitrarily divisible,
indefinitely diffuse substance, but must consist of
discrete particles. By counting the light flashes, it
became possible to determine how many single
atoms constitute a definite quantity of helium; a
new method of determining Loschmidt's number.
The results again confirmed those obtained by
other methods; this confirmation is evidence that
each of these small light flashes actually does come
from a single (electrically charged) helium atom.
Of even greater significance was still another
process, in which again the effects of single atoms
(or "ions", as electrically charged atoms are usu
ally referred to) became visible. A moisture satur
ated atmosphere is produced in a carefully cleaned,
dust-free vessel If the size of the container is
76
TWENTIETH CENTURY PHYSICS
suddenly increased by means of a moving piston
the saturated atmosphere cools off and become
"super saturated" the water vapor begins to con
dense to liquid droplets. But the first droplets
require "condensation nuclei" on which to form,
and by removing all very fine particles (dust, etc.)
we have eliminated the usual nuclei. If an alpha-
radiation from a radioactive preparation strikes the
atmosphere of this "Wilson Cloud Chamber", each
of the rapidly traveling helium ions produces a fine
track, along which are present innumerable atoms
or molecules, now likewise electrically charged,
which were hit by the alpha particles shooting
through the air. Along the entire path these newly
produced ions form suitable condensation nuclei;
the entire path appears marked as a fine streak of
mist visible to the naked eye. Again the effect of
a single charged atom and this time still more
beautifully and definitely than by scintillations
has become visible, and again calculations from
such "cloud tracks" yield Loschmidt's number.
The Wilson chamber has become one of the most
important research tools of modern atomic physi
cists. Obviously its usefulness is limited to very
rapidly flying particles, since only these possess
sufficient energy to "ionise" innumerable other
atoms or molecules along long paths. But in the
processes connected with radioactivity these par
ticles appear under various circumstances; and the
Wilson chamber presents a beautiful opportunity
to study all the details of the processes associated
with their formation and transformation.
Geiger's development, the counting tube, is an
77
TWENTIETH CENTURY PHYSICS
equally important tool for atomic physics for
determining effects of single, isolated atomic par
ticles. As soon as a single rapidly moving electri
cally charged atom enters this apparatus a macro-
physically perceptible electric charge is produced
by an ingenious arrangement. Like the Wilson
chamber this apparatus makes it possible to estab
lish the reality of atoms, to determine Loschmidt's
number and to study thoroughly atomic physical
processes.
5. Contributions of Atomic Physics. Before
Millikan's determination of the elementary electric
charge, electricity notably through investigations
by Lenard had been represented in pure culture,
so to speak, namely in the form of cathode rays
formed in a highly evacuated electric discharge
tube also in an X-ray tube, for example, where
they produce X-rays by impinging on a solid plate.
These cathode rays consist of a flow of negative
electricity; from the results of Millikan's experi
ment it is certain that this electricity must flow in
the form of separate, indivisibly small particles.
These particles have been named "electrons"; they
might also be designated as the atoms of electricity.
The cathode ray which travels rectilinearly when
undisturbed can be forced into a curved path
through the use of electric and magnetic fields.
The motion of an electron deflected under the
influence of known electric or magnetic fields must
be calculable by Newton's second law force equals
mass times acceleration if we know the ratio of
its charge to its mass, since the acting force is
proportional to the charge on a single electron.
78
TWENTIETH CENTURY PHYSICS
Conversely, this relation of charge to mass can be
inferred from the experimental determination of
the deflection of cathode rays in electric and mag
netic fields.
Since the charge on an electron is known from
Millikan's experiment (naturally from the outset
it is assumed highly probably that the electrons
in a cathode ray possess a single Millikan elemen
tary charge, not two or three; further experiments
confirm this as fact) the mass of an electron can
be calculated from the measurements on cathode
rays. The result shows that the mass of an elec
tron is about 1838 times smaller than that of a
hydrogen atom; or, expressed in grams, equals
0.9 x 10" 27 (0.9 divided by a 1 with 27 zeros after
it) grams.
The method of determining the ratio of charge
to mass with cathode rays can also be extended to
electrically charged atoms, ions. We know that
from hydrogen atoms only one type of ion can be
formed a particle which has almost the same
mass as the hydrogen atom itself and possesses
exactly one positive elementary charge. Two dif
ferent forms of ions each of almost the same
mass as the atom can be formed from the helium
atom; one has a single positive elementary charge,
the other has two. The impression results that
the electrically neutral hydrogen atom contains
positive and negative charges within its structure.
Obviously hydrogen contains just a single positive
and a single negative electric charge; and the nega
tive one must be connected with a proportionally
minute mass, whereas almost the entire mass of the
79
TWENTIETH CENTURY PHYSICS
hydrogen atom is attached to the positive one. The
supposition is suggested and abundant experience
raises it to certainty that the negative charge in
the hydrogen atom is just a negative electron. The
positive hydrogen ion, from which no further elec
trons can be separated, is designated as the "nu
cleus" of the hydrogen atom; it is also referred to
as a "proton". In the helium atom two negative
electrons are needed to neutralize the positive
charge of the "nucleus"; here again ionization of
the atom means simply the removal of one or both
electrons. The nucleus of the helium atom is,
moreover, identical with the aforementioned alpha
particles.
As Rutherford recognized, the structure of all
atoms is similar to these. In each atom almost
the entire mass is concentrated in a positively
charged nucleus; the effect of the "envelope" or.
"cloud" of negative electrons surrounding this nu
cleus is to render the atom electrically neutral.
Thus the number of these electrons must always be
equal to the "nuclear charge number"; i.e., equal
to the number of positive elementary charges in
the heavy nucleus. Chemists have known for a
long time that a very convenient view of the chem
ical elements can be obtained through their arrange
ment in the "periodic table of the elements"
wherein the elements are arranged (Meyer and
Mendeleef ) according to their atomic weights. It
was later shown that the atomic weight is not the
characteristic by which the various chemical ele
ments are differentiated; many examples today il
lustrate that atoms of different atomic weights can
80
TWENTIETH CENTURY PHYSICS
belong" to the same element (isotopes) and that
atoms of equal atomic weights can belong to differ
ent elements (isobars). Not the mass of the
nucleus, but its charge really determines the chem
ical nature of an atom; for the atomic number
(nuclear charge number) determines the structure
of the electron shells since it dictates how many
electrons the neutral atom must possess. Through
the structure of the electron shells the chemical
properties are determined. Chemical molecules are
formed when two or more atoms combine; in the
combination the outer rings of electron shells ex
perience certain transformations, but the nuclei-
remain unchanged.
The size of an atom can be determined in many
ways. Their diameters are all equal to about 0,1
millicron. These diameters cannot be specified by
exact numbers like the masses can, since the atoms
are certainly not smooth spheres with definitely
defined surfaces. As in a cloud with blurred boun
daries, in an atom only an approximate value can
be specified for its diameter. Such values can be
determined from crystals, in which the atoms must
be packed together very closely. From investiga
tions of gases it is possible to obtain corresponding
determinations of these atomic magnitudes. The
atomic nuclei are very much smaller; perhaps a
hundred thousand times smaller in diameter than
the atoms. Thus, almost the entire volume of an
atom is occupied by the electron shells. But an
electron is essentially no larger than an atomic
nucleus. How it is possible that despite this, in
a hydrogen atom for example where the entire
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TWENTIETH CENTURY PHYSICS
"shell" consists of only one electron, the volume of
the entire atom is "filled" tip by this electron is a
question to which we must return.
While chemical processes involve only the outer
electron shells, there are other processes in which
the nuclei themselves experience transformation,
division or synthesis. In the main these are the
already noted processes of radioactivity; but also
numerous artificial, arbitrarily produced transmuta
tions have been produced in atomic nuclei in recent
years. Thus the nuclei must also be represented as
complex structures; today we trace all nuclei back
to two building stones, one of which is the already
described proton and the other the "neutron" a
particle which has nearly the same mass as a pro
ton but is electrically neutral.
82
CHAPTER IV
THE PARADOXES OF QUANTUM
PHENOMENA
1. Light Quanta. It may appear on the basis
of the facts described in the last chapter that
physical research had almost completely confirmed
what had been anticipated beforehand by the
Greek philosophers of the materialistic school
even though differences exist in the manner of
notation and expression; for example, we do not
use the word "atom" today for an indivisible
structure, but rather for one which is built up of
still smaller parts. We compare, not what we
call "atoms", but electrons, protons and neutrons,
with the atoms of the Greeks. But the field of
research which appears so clear and obvious
through the results treated in the last chapter
received unexpected, new complex stimulation from
further investigations. There is irony in this
development, since the discovery of these new,
confusing facts preceded the real proof for the
reality of atoms. In 1900 Max Planck made the
discovery that directed atomic research along new
paths and opened to the theoretical and experi
mental work of physicists a tremendous new realm
for research. Thus the most important develop
ments for atomic physics were crowded together
at the turn of the century: and at that time there
appeared the criticism, based on Positivism, of
atomistic ideas developed until then. First Ernst
83
TWENTIETH CENTURY PHYSICS
Mach made it clear that in reality the atomistic
hypothesis was still completely without proof and
totally unnecessary at that time. However, shortly
after 1900 the first experimental proofs for the
reality of atoms were accomplished. In 1900
Planck had already made the discovery whose
real meaning" was grasped only a few years ago
and from which we gradually realized that atoms
are entirely different from what old philosophers
thought they were.
The wave theory of light is distinguished from
the "corpuscular theory" of light embraced by
Newton whereby light is said to consist of a
shower of very fine particles, "corpuscles" by the
proposition that the energy of light is subdivided
continuously at pleasure. This proposition ap
peared to be confirmed by primitive experience, as
had that of the unlimited divisibility of matter.
In the region of the planet Neptune the same
amount of light energy which illuminates one
square centimeter on the earth's surface has
spread out over a surface of 900 square centi
meters; arrived in the vicinity of Sirius this light
energy has spread out so far in space that it
illuminates about 10,000 square kilometers of sur
face, yet within the limits of the differentiation
ability of the human eye this distribution is still
quite uniform, as is seen inversely in the radia
tion coming to us from Sirius. The sparkle of the
fixed stars is due to disturbing effects in the
earth's atmosphere; an observer on the moon
would see these stars shine with regular brilliancy.
The wave theory of light, according to which light
84
TWENTIETH CENTURY PHYSICS
is propagated continuously through space, main
tains that this expansion of light energy can be
continued indefinitely.
But there are experimental results which con
tradict this idea. Let us consider the "photoelec
tric-effect", the regularities (Lenard, Einstein)
of which can be explained briefly as follows: if
ultra violet light of sufficiently short wave length
impinges on a metal surface, a constant emission
of electrons from the illuminated metal takes
place. The remarkable thing is that with a de
crease in light intensity the number of electrons
emitted per second decreases correspondingly
but the velocities of the individual electrons re
main constant. If the wave theory of light is cor
rect, we must conclude that the electrons torn
loose from the metal can possess less energy, the
less intense the light is just as branches are torn
off with less force, the weaker the wind blows.
But actually, with constant wave length, no more
rapid electrons are produced by the strongest light
intensities than by the weakest.
This might still be understandable if the single
electrons gathered energy from the light waves
until they had received a definite amount before
shooting out. But then a finite time would have to
elapse for very weak light intensity before the
emission of the electrons could begin. This is
also not the case. Remarkable experiments were
performed; a low intensity light source was set
up so that it would take hours fqr a single elec
tron to obtain the amount of energy the emitted
electrons actually possess. Even under these con-
85
TWENTIETH CENTURY PHYSICS
ditions not even the smallest measurable interval
of a second elapsed between the beginning of the
illumination and the beginning of the electron
emission. We do not acknowledge that something
completely unintelligible for the wave theory of
light has occurred here; yet it appears that New-
ton was somehow right, and that the incident
ultra-violet light is to be compared to a hail
shower, its energy being concentrated in innumer
able corpuscular particles.
It was also possible to determine the exact law
of this concentration of energy from the photo
effect. A monochromatic ray of light (which ac
cording to the wave theory includes just one wave
length) by this theory merely possesses equal
'light quanta", each of which contains an amount
of energy that is proportional to the wave length;
or, otherwise stated, proportional to the frequency
(number of light vibrations per second) of vibra
tions. The ratio of light quantum energy to fre
quency of vibration is the same for all light
quanta; it is designated by the letter h (Planck);
this famous quantity which controls all of modern
physics it is called the Planck quantum of action
has the value of 6.6 x 10~ 27 (6.6 divided by a 1
with 27 zeros after it) erg-seconds and the dimen
sion of "action" (energy times time). Newton of
course was not aware of this connection between
the energy of light corpuscles and frequency and
he could not have found it, since it is not a state
ment which fits into a light theory which ap
pears internally incontrovertible, but rather, pre
sents a connection between two different, diamet-
86
TWENTIETH CENTURY PHYSICS
rically opposed theories of light; the wave theory
on one hand and the corpuscular on the other.
The presence of these light quanta in radiation
can also be recognized in the radiation itself; not
in as tangible, lucid a form but as the result of
more profound considerations and experiences.
Consider a black walled vacuum vessel; if the
walls are held at constant temperature the ves
sel will be filled up with electromagnetic radia
tion. For these black walls constantly emit a de
finite radiation only heat radiation at lower
temperatures, but also visible light at higher tem
peratures, as is seen in a glowing iron. The radia
tion constantly emitted by the walls of the vessel
is absorbed again upon reaching the bounding
wall, but a certain amount of radiation energy
will remain present permanently. The problem,
upon solution of which Planck discovered his
quantum of action, is this: what is the intensity
distribution in the radiation (usually called "black
body radiation") which fills this hollow volume?
What proportions of infra-red, red, yellow, violet,
ultra-violet radiation are contained therein and
how is their intensity divided among the various
wave lengths of the spectrum when this radia
tion is resolved spectroscopically?
This problem had already been attacked ex
perimentally and theoretically by many investi
gators before Planck. The theoretical investigation
had led to a remarkable obstacle. It had been
shown that the "kinetic" theory of heat answered
this problem definitely; if the most fundamental
principles of physics are correct and the kinetic
87
TWENTIETH CENTURY PHYSICS
interpretation of heat phenomena is admissible, a
definite law must hold for the spectral resolution
of black body radiation. This law was called the
Rayleigh- Jeans radiation law. Its theoretical deri
vation depends upon considerations which make
it possible to compare the average energies of the
different light waves in a black cavity with the
average energies of single atoms in gases or solids.
The Rayleigh-Jeans law was actually confirmed
for the infra-red side of the black body radiation
spectrum. (More exactly, these are the facts: the
Rayleigh-Jeans radiation law is valid at a fixed
temperature of black body radiation i.e., of the
container walls for a part of the spectrum, from
the longest wave lengths down to and including
part of the region of shorter wave lengths. The
higher the temperature becomes, the further the
range of validity of the Rayleigh-Jeans law is
extended toward the shorter wave lengths.) From
this experimental confirmation of the Rayleigh-
Jeans law on the infra-red side of the black body
radiation spectrum another possibility was pre
sented for the determination of Loschmidt's num
ber; for from measurements on black body radia
tion it can be inferred how great the average kine
tic energy of the atoms must be at certain tem
peratures.
Actually, however, the Rayleigh-Jeans law is not
absolutely valid; the further we go from the
longer toward the shorter wave lengths the less
exactly this law is fulfilled. At very short wave
lengths the difference becomes serious. The Ray
leigh-Jeans law produced an absolutely erron-
88
TWENTIETH CENTURY PHYSICS
eous result for very short wave lengths; accord
ing to it the short wave lengths must possess so
much energy that the total black body radiation
summed up from very large wave lengths to in
finitely small ones becomes infinitely great. If this
is to be taken as striking proof for the falseness
of the Rayleigh- Jeans law (in relation to short
wavelengths), Jeans' expedient there is no real
black body radiation; cavity radiation can only
be partially black (with respect to the longer
waves) must be considered. But then the black
walls would send radiation energy into the cavity
unlimitedly; the energy of the spectral region
within which black body radiation is already pres
ent would continue to increase with time and more
and more radiation would be piled up in the short
wave length region. These conclusions contradict
our experience and the physical theories which
lead to the Rayleigh-Jeans law must necessarily
be in error. This is of serious import for physical
theory because no special hypotheses had been re
quired for this law, now proven to be false. A
revision is necessary in the most primitive, funda
mental assumptions and ideas of our physical
theory.
Planck, who discovered the true law of black
body radiation was forced to new and curious
considerations to be able to interpret the law he
had formulated.
Essentially his new ideas although at first he
sought to formulate them with as much caution
and restraint as possible meant nothing else than
a radical break with the wave thepry of light; the
89
TWENTIETH CENTURY PHYSICS
light quanta produced experimentally by the photo
electric-effect were also necessary on the basis
of Planck's observations.
The concept of light quanta solves the difficul
ties of the Rayleigh- Jeans law quite simply; a
constant increase of intensity at the short wave
length end of the spectrum is prevented by at
tributing high energy to the light quanta cor
responding to short wave lengths (high vibration
frequencies). ,
Investigation of the Compton effect gave im
portant verification of the light quantum theory.
According to the Maxwell theory of light, when
a light wave spreads over free, unbound electrons
the following must result: the electrons are in
duced to periodic oscillation through the periodi
cally varying electrical forces of the light waves.
In turn, each of these oscillating electrons will
then like a small radio transmitting antenna
emit new electromagnetic radiation In all direc
tions.
This is referred to as a "scattering" of the
radiation incident upon the electrons; part of the
energy of the primary radiation is deflected
from the original direction of propagation
and is divided in all directions around the
"scattering center". When this process is in
vestigated experimentally by the use of light with
very rich energy quanta (for the effect to be
noticeable, X-ray "light" must be used) the re
sults fall beyond the bounds of the electromag
netic wave theory of light and again clearly
demonstrate the presence of light quanta. An in-
90
TWENTIETH CENTURY PHYSICS
crease in wave length of the scattered light is es
tablished. (According to the above explained pro
position, the scattered radiation should have
exactly the same frequency of vibration as the
primary radiation since the frequency of the scat
tered radiation is determined by the frequency of
the "antenna", of the electron, and the electron os
cillates in the same rhythm as the primary wave
exciting it.) In its quantitative regularity the in
crease in wave length of scattered radiation (dis
covered by Compton) permits recognition of the
physical process which limits it. The validity of
the inferences concerning this was later verified
by further experiments utilizing the more refined
methods of the Wilson cloud chamber, the counting
tube, etc. Today we are certain that collisions of
light quanta and electrons are the basis for the
Compton effect. The single process of this phe
nomenon appears as follows : a single light quantum
impinges against an electron. The electron is dis
placed in its motion by the collision and the light
quantum is deflected from its original direction
of flight. The collision proceeds according to the
laws of elastic impact; i.e., the total energy of both
bodies after impact is the same as before impact;
the "center of gravity principle" or the principle
"action equals reaction" is also valid.
This latter principle (called the center of gravity
principle or the principle of conservation of momen
tum) is as important for modern physics as the
principle of the conservation of energy. Like the
energy principle, the momentum principle was first
recognized and formulated in mechanics. The de-
91
TWENTIETH CENTURY PHYSICS
signation "center of gravity principle 55 stems from
the following description of its effect: an accelera
tion of the common center of gravity of several
bodies can never result from mechanical reciprocal
action of these bodies; e.g., with all the mutual ac
tions of the sun and planets the center of gravity
of the system (which almost, but not exactly, co
incides with the center of gravity of the sun) al
ways retains its uniform rectilinear motion relative
to the fixed star heaven. Or when a cannon is
shot, the same force is exerted on the cannon as on
the projectile, but in the opposite direction. From
this formulation (equivalent to the other one)
there results the expression "action equals reaction".
Moreover the relativity theory, the results of which
are indispensable for the quantitative understanding
of the regularities of the Compton effect, demon
strated that this principle of the conservation of
momentum is intimately related to tthe energy
principle.
Thus the collision of light quantum and electron
proceeds according to the laws of conservation of
momentum and energy. If the direction of flight
of a single one of the scattered light quanta is
known, the direction of motion of the electron hit
by this quantum can be calculated exactly. It has
been confirmed experimentally that for each elec
tron struck one light quantum is scattered (Comp-
ton-Simon, Bothe-Geiger).
2. Quantum Transitions. In the observation
of a non-luminous Bunsen flame containing a little
sodium vapor (common salt introduced into the
flame) through a prism or diffraction grating, the
92
TWENTIETH CENTURY PHYSICS
spectrum shows only a single line 1 in the yellow;
the entire visible portion of the light includes only
the one wave length corresponding to this line.
Conversely, if light, shown by spectroscopic analysis
to contain all visible wavelengths is passed through
sodium vapor the only light absorbed is that cor
responding to this yellow spectral line; the sodium
vapor transmits all other visible light. This famous
discovery of Kirchhoff and Bunsen became the
foundation of "spectrum analysis". Like sodium,
every other neutral element possesses characteristic
spectral lines in the visible region, however, not
a single one like sodium, but usually a large
number of lines; e.g., iron has several thousand
lines in the visible spectral range alone, and for
each element there are additional lines in the infra
red and the ultra-violet. Small displacements of
spectral lines and resolution of a single line into
several closely adjacent ones can be obtained by
exposing the light-producing atoms to the influence
of electric or magnetic fields (Stark effect, Zeeman
effect). But with this exception the spectral lines
of each element are rigidly defined; therefore, the
elements present in the flame can be determined
from the investigation of the spectrum of a flame.
For chemists this has become one of the most
important methods of detecting very minute traces
of elements.
Light sources in which molecules rather than
atoms produce the light have shown that each type
of molecule possesses a definite characteristic spec
trum.
1 Actually a pair of limes.
93
TWENTIETH CENTURY PHYSICS
Spectral analysis became a most important, fruit
ful aid to astronomy. The spectra of stars and
nebulae contain chiefly the same spectral lines which
we can produce by introducing different elements
into terrestrial light sources. Fundamentally this
furnishes proof that the entire stellar world is
composed of the same chemical elements we have
become familiar with on our earth. Furthermore,
investigation of stellar spectra yielded an abun
dance of knowledge concerning the physical nature
of the different heavenly bodies and the conditions
to which luminous atoms are exposed therein.
Particularly, several lines were found in stellar
spectra which as an exception to the rule could
not be reproduced in any laboratory on the earth
and furnished evidence that matter exists there
under conditions which cannot be imitated in the
laboratory (e.g., gases of absolutely tremendous
rarefaction). Even in these cases there appear
no chemical elements other than those known from
earthly experience. Spectra furnished more refined
and more abundant information on the nature of
atoms, than any other method of investigation.
It seems apparent that there is more to be learned
about the nature of the iron atom from the spectrum
with its many thousand lines than from the little
numerical data concerning mass, atomic number
and approximate size of the atom. But first it
was necessary to understand the language of these
spectra, and that was not at all easy. That inner
motions of the atoms were betrayed on the outside
through light emission was not surprising in itself;
for it is known that the constituents of the atom
94
TWENTIETH CENTURY PHYSICS
are electrically charged and in motion must act
like a small antenna. But it was not possible to
interpret the regularities of the spectra through
an explanation of the radiation concept based on
the principles of classical mechanics and electro
dynamics. Careful analysis demonstrated simple
and beautiful mathematical regularities in the
spectra. The spectral lines of hydrogen, for ex
ample, can be represented in wonderfully simple
mathematical formulae (Balmer, Lyman, Paschen) ;
and Ritz formulated a quite general mathematical
law (named after him) of very simple form for
all elements. But it was shown to be impossible
to obtain a physical explanation of these empirically
determined regularities on the basis of the physical
concepts established before 1900, the basic ideas
of which we attempted to explain in the preceding
chapters. Despite its important contributions to
chemistry and astronomy all spectral investigation
remained completely outside the theoretical struc
ture of physics of that time. The regularities
found by Balmer, Ritz and others, which were riot
self-explanatory, remained with all of spectroscopy
in the museum of physical science.
This condition was altered by the development
of the quantum theory from Planck's discovery, first
hesitantly and in later years more and more rapidly
and forcefully. In 1913 Niels Bohr demonstrated
the possibility of explaining the hydrogen spectrum,
the simplest of all spectra, on the basis of the
quantum theory; and beyond that of understanding
the general Ritz principle through this same theory.
Since then the extremely rich development of Bohr's
95
TWENTIETH CENTURY PHYSICS
Ideas showed wonderful fruitfulness. With the
close reciprocal action of theoretical thought and
further experimental research our knowledge of
spectra increased to a tremendous extent; simul
taneously also the meaning of their obvious regu
larities gradually became clear. To grasp a few of
the principal points of this development it will
again be necessary to disregard historical se
quence.
The so-called "electronic-impact experiments"
of Franck and Hertz led to conclusions as funda
mentally surprising as the discovery of light quanta.
In these experiments the atoms of a gas or vapor
were bombarded with electrons, the velocity of
which was controllable and known precisely and
it was shown that with very slow electrons the
collisions are always strictly elastic.
If any macrophysical system capable of internal
oscillation is struck a blow from the outside, the
system enters into more or less vigorous oscillation.
The energy content which the system removes from
the impinging body and absorbs as internal energy
can assume all possible values from zero to the
total energy of the striking body ; a very weak blow
from an energy-poor body can only transfer a little
energy; but there always remains the possibility
of a second, weaker collision wherein a still smaller
amount of energy is transferred. In all cases it
is "infinitely improbable" that no energy at all is
transferred; thus, the collision is exactly "elastic".
The Franck-Hertz experiments show that an
atom behaves quite differently in this respect.
Electrons of very small velocity can not convey
96
TWENTIETH CENTURY PHYSICS
internal energy to the atom at all; an atom never
takes up such a small amount of energy. The
electron must possess a certain minimum amount
of energy if the atom is to take up any from it in
its internal system and then it removes all this
energy from the electron, never only a part of it.
If the kinetic energy of the electron is a little greater
than this minimum the atom always withdraws
from the hitting electron (if at all) only exactly
this minimum amount of energy. If the electron
has still greater energy the atom can take from it
at collision certain (definite) greater quantities of
energy.
In the macrophysical system the energy con
tent has a certain value which can vary continu
ously; but in the atom the energy content is not
capable of continuous change. Instead there exist
definite "energy levels" for the atom. The mean
ing of this phrase will become clear directly since
we can illustrate the difference between continuous
ly and discontinuously changing energy through
comparison of an inclined, smooth path with a
staircase. But one must not assume that the
energy levels (steps) of an atom follow each other
with equal separation. As a matter of fact these
separations vary within an atom; and besides, the
position of the various energy levels is quite dis
similar in the different elements. Each element
possesses an infinite number of such levels, com
pressed closer and closer together on top to a
certain limit; should the atom take up more energy
than corresponds to this upper limit of energy levels
it must become "ionized" an electron Is torn out
97
TWENTIETH CENTURY PHYSICS
of Its electron shell and flies forth with the sur
plus energy. This ionization of an atom through
the impact of a sufficiently high speed electron had
already been discovered for a few cases by Lenard;
but for us here the energy levels below the "ioniza
tion limit" are far more important.
The paradox of this result is obvious: one can
not imagine a fact which smacks in the face more
brutally all the concepts on which classical physics
is based. The principle of continuity is pierced.
Since it is established that an atom can never possess
energy levels other than those which correspond
exactly to those valid for this atom, we must re
solve, consequently, that changes of energy also
can no longer follow continuously. Therefore the
atom is no longer the same as a macrophysical
structure, the energy content of which Increases
and decreases continuously. A change of state
through which an atom shifts from one of its pos
sible energy levels to another one is a discontinuous
elementary process, a "quantum transition". Na
ture makes transitions!
Paradoxical as these conclusions are, they agree
harmoniously with the equally paradoxical deter
minations we were forced to make concerning the
nature of light. We have now learned that an
atom changes its Internal energy in discontinuous
jumps. We learned earlier that the energy of a light
ray in sharp distinction to the assertions of classi
cal wave theory is concentrated in individual light
corpuscles. Both paradoxes fit together. We arrive
at the conception that light production by atoms
proceeds in such a way that an atom in a quan-
98
TWENTIETH CENTURY PHYSICS
turn transition changes its energy discontinuously
and emits the energy that has been freed in the
form of a light quantum. The absorption of light
is the exactly opposite process. This concept was
checked and confirmed in all its inferences by
Franck and Hertz (and after them by many other
physicists) in an abundance of experimental tests.
Through it we can calculate all the spectral lines
of an atom from a knowledge of its energy levels;
and the converse, since we know that a light
quantum of a certain energy (as it results from
a quantum transition in an atom corresponding
to an energy change of the atom) also possesses a
quite definite wave length which can be calcu
lated from the energy according to the above
relation. It was also pqssible to determine directly
by experiment that atoms which have been raised
to a definite energy level, perhaps by electron im
pact, emit from the possible spectral lines of the
element in question just those for which, accord
ing to this concept, the energy level in question is
the "initial condition". Energy transfers between
two colliding atoms had also been observed; here
simultaneously the one atom jumps to a higher,
and the other to a lower level The possible re
maining energy surplus is converted into kinetic .
energy of the separating atoms. These are only
quite fleeting hints; but that the above idea
gained from the existence of light producing (or
light absorbing) processes is correct has become
an irrefutable certainty through modern experi
mental measurements.
3. Dualism; Waves Corpuscles. We inter-
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TWENTIETH CENTURY PHYSICS
rupted our consideration of light phenomena be
fore we succeeded in finding a solution of the con
tradiction between the wave and corpuscular
theories of light which were established reliably
through experiments and which both represent in
escapable results of experiment. But they mutu
ally contradict each other; and instead of a solu
tion of this contradiction we have as yet seen
no further than a combination, an arrangement
between the two mutually contradictory theories in
the form of a relation which permits the proper
wave length to be calculated from the energy of
a light quantum, or vice versa.
The paradoxes only increase when we realize
that this same incomprehensible anomaly also
appears in other radiations. We know that
cathode rays really consist of a flow of electrons;
yet if these cathode rays are passed through crys
talline foils, there result interference phenomena
analogous to those produced by X-rays. The dis
covery of these interference effects was so amaz
ing and unexpected in view of our previous cer
tainty of the corpuscular nature of cathode rays
that at first it was disregarded by experimental
physicists. The wave properties of cathode rays
like the Maxwell-Hertzian waves were first pre
dicted by theoreticians. It was de Broglie who ar
rived at the bold idea that the "dualism" of waves
and corpuscles with which we became familiar
in light could also be found in cathode rays and
other material radiation. De Broglie was able to
show that if such an effect is actually present the
corresponding wavelengths in the cathode ray
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TWENTIETH CENTURY PHYSICS
must be defined by very simple theoretical laws
(for the detection of which the theory of relativity
was again extremely important).
Only several years after de Broglie's theoretical
disclosures were these paradoxical suppositions
checked experimentally. The result was positive;
the interference effects predicted by de Broglie
were exhibited for cathode rays. Later these ex
periments were even performed with corpuscular
rays with a stream of atoms; here the proof of
the wave properties is still more difficult because
the wave lengths are much shorter than for elec
trons (cathode rays) of the same velocity. Ac
cording to de Broglie the wave length correspond
ing to corpuscles at a certain velocity is inversely
proportional to their mass. Today we can no
longer doubt that this dualism of waves and
corpuscles is a quite general physical regularity;
each wave radiation which takes place must sim
ultaneously be a corpuscular ray and each cor
puscular ray must on the other hand also exhibit
wave properties. Practically it is only for light
and the lightest corpuscles that it is possible to
grasp both sides of the phenomenon with our pres
ent experimental methods. For all other cases the
de Broglie mathematical formula yields results
for the correspondence of waves and corpuscles
which lie beyond the possibilities of practical ob
servation due to their minuteness. This is just
what is to be desired; only in the realms of ato
mic phenomena is there, room for dualistic phen
omena; it would be a gross contradiction of ex
perience for a theory to maintain that these dual-
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TWENTIETH CENTURY PHYSICS
istic phenomena also occur in the macroscopic, that
corpuscles are perhaps evident in radio or sound
waves or that conversely interference effects re
sulted when a machine gun was shot against a
garden lattice.
The paradox of this dualism requires no em
phasis; here we are faced with phenomena which
are completely inconsistent with the ability of
our classical physical theories for intellectual re
production. Let us consider a concrete example.
In a black, light-impervious screen two very small
openings are introduced close to each other. Light
from a point source passes through these on to
a photographic plate set up some distance away.
The intensity distribution of the light striking
the photographic plate is recorded on it. For suffi
ciently small openings (and sufficiently small se
paration between them) the result is not two light
spots on the -photographic plate as would be ex
pected from exact rectilinear propagation accord
ing to geometric shadow construction; the two
light rays which come through the two openings
interfere with each other.
There was discussion of the supposition that
the intensity distribution on the photographic
plate would change if the light intensity were made
infinitesimally small so small perhaps, that on
the average only one light quantum would be
emitted from the source per second. For it is
naturally an obvious expedient to attempt to ex
plain the interference effects as a result of a
mutual action of different light quanta upon one
another. One would then have to imagine that
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TWENTIETH CENTURY PHYSICS
the light quanta which passed through the one
opening reacted mutually with those which went
through the other opening, the interference re
sulting from their interaction. But the inevitable
consequence that the interference effect must be
destroyed for very small light intensities where
the light quanta occur individually and can not
combine in any way was not confirmed by ex
perience. Regardless of whether the photographic
plate is very strongly illuminated through the
screen openings for a very short time or whether
if is illuminated for a correspondingly longer
time with weak intensity exactly the same diffrac
tion pattern is formed on it.
Thus we can not do otherwise than imagine
that interference laws apply to the individual light
quantum. Naturally a single light quantum emit
ted by the source can only be absorbed in a
single grain of the photographic plate. Intensity
distributions which appear continuous to- the
rough view can therefore occur only if large num
bers of light quanta are absorbed. Here we must
revert to the concept of probability; we must say
that one single light quantum emitted by the source
possesses a certain probability that it will appear
at the exact position of the plate we are viewing;
and this probability is given precisely by the light
intensity at the point of the plate in question
calculated according to classical wave theory.
But how does the light quantum reach there from
the light source? Previously we emphasized that
a self-evident provision of classical Galileo-New
tonian mechanics lies in the conviction that a
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TWENTIETH CENTURY PHYSICS
physical body cannot reach a place from another
except by traversing a continuously connected path
between these two points. But how can this be re
conciled with the interference considered in our
example from which we know explicitly that
interference is not only shown for a light quan
tum, but likewise appears in principle for material
particles like electrons and atoms? The answer
we must resolve to accept is that this cannot be
reconciled and that we must regard this self-
evident provision of classical mechanics as a pro
position in plain disagreement with atomic and
quantum physics. It is only possible to define the
path along which a particle moves continuously
insofar as interference phenomena are absent;
where interference stands out perceptibly the use
fulness of this classical concept ceases funda
mentally.
As enigmatical as these facts are and as much
as they contradict all our thought and visualiza
tion habits, it should be understood that in a cer
tain sense the picture of nature is simplified by
this dualism. Formerly we believed that there were
both wave and corpuscular radiations in nature;
and our classical viewpoint let us consider them
as completely and irreconcilably different Now we
see that, in reality, nature recognizes only one
kind of radiation which could not be imagined on
the basis of classical physics, since on the one
hand it exhibits properties which correspond to
our classical wave representation but on the other
hand corresponds to the classical representation of
a corpuscular ray.
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TWENTIETH CENTURY PHYSICS
We admit that we still have not understood the
thing, and make it clear that from these deter
minations the previously disclosed phenomena be
come more understandable "more understand
able" in the sense that in any case we recognize
connections between them and the paradoxes be
ing discussed now. It has been mentioned that the
spatial extent of both the atomic nucleus and the
electrons is about a hundred thousand times smal
ler in diameter than an atom the hydrogen atom
for example. Now we resume consideration of
a problem introduced then how it is possible that
the one electron in the hydrogen atom, despite
its small size, can "fill up" the relatively enor
mous space of this atom. According to our pres
ent knowledge the electron must also be imagined
as a wave and this problem becomes quite dif
ferent. Now we must imagine that the charge of
the electron, in the sense of the de Broglie wave
theory, is somehow "smeared" over the entire
volume of the atom, so that this single electron
actually forms a "cloud" of electrical charge.
There is also a fact connected with the dual
ism of waves and corpuscles which in a suitable
characteristic manner distinguishes the modern
quantum theory corpuscular concept from that
of the indestructible atom in Greek philosophy.
Electrons (and the same holds for all other cor
puscles) possess no "individuality".
Two widely separated electrons may approach
each other, meet, separate again and return to
their original positions. It can never be deter
mined whether "the same" electron has returned
105
TWENTIETH CENTURY PHYSICS
to that position or an "exchange" of the two has
taken place it must immediately appear sense
less, considering the previously described criticism
of physical statements, to pose this problem at
all, to desire a yes or no answer to it. For fun
damentally all criteria are lacking which could
lead to a choice between the alternatives. We
must imagine all electrons as completely equal;
and it is not possible to place an "identification
mark" on an electron in any way. Thus far we re
main in harmony with classical atomic philosophy.
But now, through the dualism of waves and cor
puscles, a new idea appears. We are no longer
to remain certain of the identity of an electron
permanently by observing its motion; when the
definition of a path becomes impossible or un
certain through interference effects, two electrons
which approach each other very closely can "inter
change" so that they can no longer be distin
guished individually.
4. The Limits of Causality. Consideration of
interference phenomena caused a modification of
the law of motion of a corpuscular particle travel
ing free of force. According to Galileo and New
ton we said earlier that a body that is not in
fluenced by an external force continues along its
path rectilinearly with the velocity it once attained.
If this were the case for light quanta, obviously
there would be no interference, no diffraction
phenomena; light quanta striking a perforated
screen would quite simply be partially kept back
by the screen and partially transmitted through
the openings, and beyond the openings they would
106
TWENTIETH CENTURY PHYSICS
move on rectilinearly the simple geometrical laws
of shadow construction would hold with unlimited
exactness, without being broken down by diffrac
tion phenomena. Instead it was necessary to
formulate the law of motion for light quanta emit
ted by the source which reached the photographic
plate through the screen openings so that it in
cluded the word "probability". We spoke of the
probability that the light quantum in question ap
pears at a certain place on the plate, and formula
ted the natural law concerning this so that the
light intensity calculated according to the wave
theory was indicated as an exact measure of this
probability. Apart from all other difficulties, this
result was in abrupt opposition to classical caus
ality which had attained such clear and convinc
ing form in the Galileo-Newton mechanics.
That we actually do not progress if we adhere
to the classical theory of causality is also in
dicated by various other facts. The radiation
which emanates from radium, as the elementary
process, is an indication of the disintegration of
the radium atom nucleus ; emission from the radium
nucleus is always in the form of an alpha-particle
(helium nucleus) and what remains is the nucleus of
another element ( radon radium emanation) . But in
a large quantity of radium atoms a simultaneous dis
integration of all the radium nuclei does not occur;
the law prevails that after 1580 years one half
of the original amount of radium has remained
unchanged; after 1580 more years half of that
half remains, and so on. The physicist. finds him
self here in the same position as the director of
107
TWENTIETH CENTURY PHYSICS
a life insurance company. Without being- able
to betray anything to the insured individual about
the probable instant of his death, the insurance
director can still recognize the statistical law for
the average time of death among a large num
ber of insured and thus can recognize reliably
that an insurance business can be established on
that basis. Likewise, the physicist knows how
many of a thousand million radium atoms, for
example, now present will disintegrate within the
next year; he does not know whether a single
radium atom presented to him will decompose
within the next second or will still survive for
millions of years. This could simply be con
sidered as the incomplete state of our knowledge;
it is possible to believe that physicists of the fu
ture will learn to place a prognosis of its
life-expectancy on a single radium atom. But the
above stated mathematical law for the "dying" of
radium atoms contradicts this idea. A simple
mathematical consideration shows that this law
is equivalent to the following determination: a
single radium atom, submitted to us today, has
a definite probability of disintegrating within the
next 24 hours. If this radium atom actually has
not disintegrated by the first of January of the
year 3000, the same probability exists then for
its decomposition within the next 24 hours as now.
The problem of radium atoms is entirely different
from that of the human being, who, having nearly
reached the age of 100 years, must expect his
death within the next month with much greater
probability than a 20 year old. It is not a
108
TWENTIETH CENTURY PHYSICS
peculiarity of living organisms that the prob
ability o death changes in the course of time;
it is merely a general result of the theory of causa
lity that we expect the probability for the disinteg
ration of a physical structure due to internal
causes to change in the course of time, since it is
determined by the previous history of this struc
ture. By contradicting this expectation the radium
atoms represent a physical event that is not con
sistent with our classical conception that each
effect can be traced back to a definite cause.
Let us consider still another example that makes
it even clearer that this denial of the classical con
cept of causality is not to be understood as a
temporary imperfection of our knowledge, but is
inherent in the nature of the thing again show
ing how incorrect our previous, classical concepts
were. Light waves were previously described a*s
transversely vibrating waves. With the aid of
a "Nicol prism" the physicist can resolve a light
ray into two component waves w;hich are "linearly
polarized"; that means that in each of these com
ponent rays the electric field intensity of the
light oscillates only within a definite plane deter
mined by the light ray. In the two component
rays these 'Vibration planes" are perpendicular
to each other; one component wave is transmit
ted by the Nicol prism, the other is reflected.
If a linearly polarised light ray impinges on a
Nicol prism again, it is resolved in general into
two new linearly polarised rays, the plane of vi
bration of which are mutually perpendicular but
are inclined to the plane of vibration of the first
109
TWENTIETH CENTURY PHYSICS
ray. The relation between the intensities of the
two component rays after this second resolution
depends upon the angle (given by the relative
positions of the two Nicol prisms) of this in
clination. If we imagine this experiment per
formed with just a single light quantum we must
say that this light quantum has two possibilities
It can be transmitted or reflected through a cor
responding rotation of its original plane of vibra
tion; the intensity relation calculated from the
wave theory of light must again give the pro
bability of realization of each of the possibilities.
If we wish to maintain the concept that some
how it is causally determined in advance which
of the two possibilities will be realized for this
one light quantum we shall become hopelessly con
fused. The angle of inclination of the Nicol prism
can be a quite arbitrary one; and besides we can
arrange an arbitrarily long row of differently
inclined Nicol prisms behind each other; it is im
possible to determine the hypothesis of which hid
den property of the light quantum predetermines
causally how the light quantum will behave in
each possible case of this kind without contradict
ing the irrefutably established probability law for
transmission or reflection expressed above. Thus
we must decide to admit that causal predeter
mination of the behavior of an individual light
quantum near a Nicol prism is not given in
nature; nature does not effect the distinction be
fore the occurrence of transmission or reflection.
110
CHAPTER V
THE QUANTUM THEORY DESCRIPTION
OF NATURE
1. Quantum Mechanics and Wave Mechanics.
We have traversed the realms of physical re
search as rapid travelers. Since we failed to take
along the heavy weapons of mathematics, we have
been limited, so to speak, to the role of a civilian
war correspondent in the land of physical re
search who must be content to draw some mood
pictures of the events there without seriously pur
suing the strategical and technical problems. We
passed by rich departments of knowledge, varied
and beautiful in their content. To omit considera
tion of the thought structures in which modern
physical thought triumphs over the apparently
hopeless paradoxes and difficulties which were
evidenced in quantum physical experiments would
require still greater decision. It is not possible to
relate and explain here the heavy weight of ex
perimental quantitative proof of the content and
mathematical laws of modern quantum theory;
a clarification of the philosophical-logical character
of this theory by intimation must suffice. But
even for that the author, who wants to make it
more easily accessible to the reader, must request
special attention.
Let us consider briefly the historical develop
ment of modern quantum theory. The investiga-
111
TWENTIETH CENTURY PHYSICS
tion of atomic spectra (and the energy levels re
lated to them) presented physical research with an
abundance of varied problems, in the step by step
clarification of which physicists gradually worked
out an understanding of the regularities of quan
tum physics. Niels Bohr, who started this de
velopment in 1913 also remained its leader.
Without going into the thousand different prob
lems of this field we shall consider the Bohr
"correspondence principle''. Although it was men
tioned in reference to the energy or relativity
principle and not opposing these in its meaning
the correspondence principle has a quite dif
ferent character from the energy and relativity
principles. These latter are natural laws in
finished, perfected form; their content can be ex
pressed clearly and thoroughly in a few words.
But the correspondence principle presents peculiar
difficulties to the intelligence since its general con
tent can only be described by intimation, or it
can be illustrated in special individual examples.
For the correspondence principle is not a finished,
clearly definable law of nature, but indicates the
direction in which Bohr's conviction about the
solution of the quantum puzzle was to be sought,
and in which he wished to steer the reflection
of the quantum investigators. It only becomes
clear in the history of quantum theory that not
only individual great discoveries are decisive for
the development of our knowledge but that under
certain circumstances the change of our spiritual
attitude toward problems can be much more im
portant. Physical thought develops not only from
112
TWENTIETH CENTURY PHYSICS
combining the compilations of results of indivi
dual observations and their logically-exact treat
ment; but rather the attainment of decisive new
intelligence depends essentially on a creative
phantasy, which for its part depends essentially
on spiritual hypotheses and on the attitude our
intuition assumes toward these things. Bohr's
historical contribution lies not only in the indi
vidual, pioneer discoveries through which he en
riched quantum theory but also in the penetrating
force his spirit exerted for the creation of a new
spiritual "atmosphere" wherein the problems
were first gradually elucidated as the essential
became distinguishable from the unessential and
effective control of the solution became possible.
The meaning of the correspondence principle
is not purely historical; it is still indispensable
today in the sense that it teaches us to view
modern quantum theory knowledge with the
proper attitude.
The differences between quantum theory and
classical physics are so deeply rooted that many
physicists were tempted to regard the ideas of
classical physics as absolutely useless for the com
prehension of atomic physics; they attempted to
introduce arbitrarily invented, new, untraditional
ideas. But Bohr had and this is the content of
the correspondence principle energetically pointed
out that in all individual problems a verifiable
close similarity exists between classical and
quantum theory despite their fundamental dif
ference. The following is a rough example:
classical physics predicts that atoms, which con-
113
TWENTIETH CENTURY PHYSICS
sist of electrically charged particles, necessarily
emit light in the execution of internal motions.
This prediction is correct. The elementary pro
cesses of this light emission do proceed quite dif
ferently from macroscopic antennae; but the fact
remains that the fundamental expectation is ful
filled. That is an example of the close relation
ship which exists between classical and quantum
theory despite their incisive difference. There are
other examples of this relationship, much finer
examples; and through Bohr we gradually learned
to see that such kindred relationships can ab
solutely be uncovered for each concrete individual
problem through more exact analysis.
In his emphasis on the affinity of classical and
quantum theory there exists, however, a decided
prominence of the independence of the quantum
theory from classical theory. Since we learn to
"understand" various quantum-physical individual
problems better through uncovering kindred rela
tionships "in the manner of correspondence", we
gradually attain one of the concepts of quantum
physics used in classical theory but separated
from it by fundamental differences and indepen
dent in itself. Such a discovery is a radical chal
lenge to the repeated spasmodic attempts through
out the course of historical development to some
how want to "explain" the characteristic quan
tum phenomena to want to reduce them to ideas
which conform more closely to the classical.
With the progress of this development it gradu
ally became clear which problems in general
should be answered by a logically effected quantum
114
TWENTIETH CENTURY PHYSICS
theory. Here the positivist consideration must
be repeated very forcefully; the goal of a purely
intellectual comprehension of quantum phenomena
must be a description of the experimental facts
themselves. The experimental facts involved here
are collectively of the following sort: a specific
atom, characterized by its atomic number, accord
ing to experience possesses quite definite energy
levels. The first problem appears; how can the
positions of all these energy levels (for any atom,
and likewise for molecules) be determined and
calculated from general theoretical principles?
Furthermore, we find "transition-probabilities"
for these atoms. When an atom exists in an
energy-rich condition, after some time it will un
dergo a quantum transition which brings it down
to a lower energy level while the energy freed
thereby comes off as a light quantum. The atom
has a range of various such possibilities since
there are different lower energy levels at its dis
posal As in the case of the radium atom de
scribed above, it is not possible to predict in an
individual case when and where the atom will
jump. But experience indicates the existence of
quite definite probabilities for the various pos
sible processes. If the atom is irradiated with
light there results a definite probability for a
quantum transition associated with the absorption
of a light quantum. If an electron of a certain
(sufficiently high) velocity impinges on an atom,
the atom can, as we already know, thus also be
induced to a quantum transition. If, further
more, the atom collides with another atom (of
TWENTIETH CENTURY PHYSICS
the same or a different kind) an energy change
can occur, as was already mentioned, in the form
of a simultaneous mutual quantum transition.
Definite probabilities prevail for all these proc
esses; based on experience they are always stated
in the same ways through the conditions of the
experiment in question* They are summarized
under the designation of "transition probabilities".
Now the problem (besides the theoretical deter
mination of energy levels) that a complete quan
tum theory must solve quite comprehensively is
simply the theoretical determination of the transi
tion probabilities.
In this sense Heisenberg undertook the creation
of a "quantum mechanics". He relied upon the suc
cess then already achieved in the detailed execu
tion of Bohr's correspondence principle; in fact,
the systematic evaluation of Heisenberg's exten
sions (Heisenberg, Born, Dirac, Jordan) yielded
a solution of the problem formulated according to
the correspondence principle which was complete
in principle. Of course the mathematical formu
lation of this solution was such that it differed
extensively from the mathematically precise ren
ditions of our classical physical conceptions. But
this mathematical form of the new quantum me
chanics was most exactly suited to thp problem (as
we stated it) of the determination of transition
probabilities. Besides, this new quantum mechan
ics expressed wonderfully the two-sided relation
of quantum to classical theory; namely, funda
mental difference on the one side and close con
nection on the other. The mathematical medium
116
TWENTIETH CENTURY PHYSICS
of representation utilized is the so-called matrix
theory a chapter of mathematics that had al
ready been cultivated for a long time by mathe
maticians for its own sake without their surmising
the importance it was to attain for atomic physics.
These investigations had just reached a pre
liminary rounding-off point when Schrodinger ar
rived at the same goal by an entirely different
method. Schrodinger started with de Broglie's
investigations. After de Broglie had shown how
the uniform rectilinear motion of a corpuscular
particle was reinterpreted in the wave theory,
Schrodinger wondered how these de Broglie con
siderations developed for motions influenced by
external forces. For this reason he investigated
the motion of an electron under the influence of
the attraction of a positive heavy nucleus ; and thus
he arrived at the quantitative description of the
electron charge, cloud in the hydrogen atom.
Schrodinger could now show that with the solu
tion of the mathematical problem he formulated
he had simultaneously also achieved the solution
for the apparently quite different mathematical
problem, which was expressed by quantum me
chanics in the form of matrix theory. Thus,
when a problem has been solved by means of
Schrodinger's "wave mechanics" a mathematical
conversion yields the "quantum mechanics" solu
tion for this same problem. This mathematical
connection between the two . theories, leading to
the same result, which in view of the complete dif
ference of the two .methods must appear very
surprising at first, also supplied the certain basis
117
TWENTIETH CENTURY PHYSICS
for the physical-abstract interpretation of Schro-
dinger waves. At first it might appear that
the discovery of wave mechanics yielded a mitiga
tion of the contrast between quantum and classi
cal theory; for here instead of the unclassical con
cepts of transition probabilities, etc., we deal with
waves something closer to classical ideas. But
what we just learned with respect to light is still
true; the classical wave theory is not the final
word. Wave mechanics does not in any way
signify for atomic physics the removal or mitiga
tion of the fundamental unclassical characteristics
of quantum physics. Also, for atoms with more
than one electron (thus for all atoms except hy
drogen) Schrodinger wave mechanics assumes a
very abstract form; in these cases Schrodinger
waves are no longer waves in customary three-
dimensional space but are simply a mathemati
cal construction which mathematicians can "illus
trate" to themselves as waves in space of more
than three dimensions. This abstract, multi
dimensional space can be avoided through an
other (mathematically equivalent) method of rep
resentation, the construction of which was a spe
cial hobby of the author's. In this method of
representation ("second quantization"), which
clings especially closely to the fundamental dual
ism of waves and corpuscles, the waves dealt with
are spread out in ordinary three-dimensional space,
but can only be described by means of the ideas
of quantum mechanics.
These theories, whose abstract nature will not
remain hidden from the reader in even this fleet-
118
TWENTIETH CENTURY PHYSICS
ing explanation, made possible a number of spe
cial uses for individual problems of atomic
physics. The precise correctness of the new theory
was confirmed without exception in a tremendous
field of experimental results. No end is in sight
for the further elaboration of special problems
on the basis of these principles. The fundamental
result may be stated as follows: today we can
understand all phenomena which occur near and
in the electron shells. Thus all the elementary
processes that are the basis for spectral or chem
ical processes are defined as clearly as the motions
of the planetary systems have been since Newton.
The only partially explored realm at present re
mains the physics of internal events in atomic
nuclei.
For us it is only important to understand the
philosophical nuclei of these new ideas. We again
owe special thanks to Bohr and Heisenberg for
the philosophical-epistemological explanation of
the meaning and significance of the new theories.
This became possible through the earlier thorough
mathematical understanding of the quantum laws
in the so-called "statistical transformation theory"
(Dirac, Jordan).
2. Objectivity. We return once again to clas
sical theory to emphasize still more clearly the
characteristic features through which it differs
from quantum theory. We can state three basic
principles which should be considered as the most
important characteristics of classical theory with
the catchwords continuity, causality, objectivity.
We spoke amply of continuity; and we learned
119
TWENTIETH CENTURY PHYSICS
that jttst this principle of continuity constitutes
a difference between classical and quantum theory.
But now we want to make it clear that continuity
is not only something familiar to us, but is really
an essential, the omission of which is followed
with logical necessity by further fundamental
deviations from classical ideas.
The assumed continuity of natural processes is
essential for our method of executing and evaluat
ing physical measurements. Every measure
ment we perform is inexact. The physicist con
siders the "limit of error" for each measurement;
for every measured numerical valu$ he records two
numbers, the difference between them correspond
ing to the uncertainty of the measurement. That
it is nevertheless possible to draw certain con
clusions from an inexact measurement conclu
sions, of course, that are also affected by an un
certainty but in any case are rich in content and
very definite is only because the principle of con
tinuity is actually fulfilled in the macrophysical
world; trivial changes in the cause are followed
by trivial changes in the effect. Consequently an
inexact knowledge of causes is still sufficient for
an inexact prediction of the effects, although the
absolutely certain prediction of the effects becomes
possible only with a mathematically more precise
(practically unattainable) measurement of the
causes.
Uncertainty in the process of measurement
deserves a still more detailed investigation. The
essential point for us here will become clear if
we visualize, for example, the measurement of
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TWENTIETH CENTURY PHYSICS
the temperature of a tnacrophysical body. We
bring the body in contact with a thermometer;
the thermometer assumes the same temperature as
the body in question; and we read off the value.
But to be exact, it is necessary to consider that
since the body under investigation imparts some
of its heat to the thermometer the body itself is
influenced and its original condition is altered
somewhat. To avoid resultant false measure
ments the thermometer selected must be much
smaller than the body being investigated. (Of
course it is possible, if the thermometer used was
not sufficiently small, to compute or estimate the
temperature change which took place and correct
the result for it; but that is a problem in technical
method which has no connection with the nature
of the thing.) It is analogous for every physical
measurement: I must always select such fine in
struments for a measurement that in the measur
ing process the body under investigation itself
will not be influenced appreciably by too rough a
measuring instrument (such influence would
falsify the measured result). Fundamentally a
reaction of the measuring instrument on the ob
ject being investigated is inherent in every physi
cal measurement; yet in the investigation of
macrophysical objects this reaction can be made
sufficiently small by the selection of quite fine
instruments. 1
This idealization of the process of measuring
1 This concept of the "fineness" of a measuring instrument
should not be understood too vaguely; not the spatial largeness
or smallness of the instrument but rather the magnitude of the
energy of reciprocal action between the instrument and the
observed object is decisive.
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TWENTIETH CENTURY PHYSICS
in classical physics depends essentially on the as
sumption of continuity of all natural processes in
the sense that our fundamental considerations are
established as though precise measurements were
possible for us. It is a "permissible idealiza
tion'' to base our considerations on this concept
of absolute observational accuracy and to interpret
the actual inaccuracy of each measurement as an
only practically and not principally significant sec
ondary disturbance. This idea cannot lead us to
errors, because by classical concepts we can ap
proach ideal measurement unlimitedly, although
we can never attain it.
We here consider something which we shall in
dicate with the word objectivity and which is so
characteristic of our general classical-physical think
ing that we usually disregard it. We are accus
tomed to regarding physical observation results as
clearly understood according to their importance
if we have explained them as effects of an objective
physical process or condition. This formulation
hides within it a higher type of positivist modesty;
a deeper "explanation" of natural processes is re
linquished herein for everything. But what is left
after this renunciation of all classical-physical
theories as a basis for their methods of represen
tation is just this idea in objective events. Per
haps we do not describe planetary motions by speci
fying when and where or through what telescope
the various planets were observed; but we do des
cribe planetary motions as a spatial-temporal pro
cess taking place independently of human obser
vation. Naturally one can pursue the familiar
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TWENTIETH CENTURY PHYSICS
philosophical considerations which emphasize that
without subjects doing the observing there can be
no talk of objective matters. But these thought
processes are not acceptable to the physicist.
To him the motion of the planet Neptune in its orbit
is an objective event which^was already in process
before anyone had seen this planet in a telescope
and which continues uninfluenced, independent of
whether or when or how often it is observed or
photographed. Exactly the same self-evident sup
position of objective events is the basis for Max-
wellian electrodynamics ; we interpret electrical
measurement data as indication of an objective
physical event in the electromagnetic field which
is present in space.
Positivist criticism must remind us that this
objectivity of physical events is not a purely logical
self-evident fact. For positivism teaches us to
view true physical reality only in the totality of
experimental results. It is very remarkable and
astonishing that in the domain of validity of
macrophysics we are in a position to so formulate
our summarizing description of experimental results
that they are no longer referred to directly but
are, so to speak, only minor appendages of the
picture we have traced out a picture which main
tains the existence of objective events which occur
independently of how and where the observations
necessary for their detection are taken.
After what has been said it is obvious that the
idea of ideal measurements (made possible by the
continuity of macrophysical processes) which do
not disturb the observed event in the least is in-
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TWENTIETH CENTURY PHYSICS
dispensable for this construction of an objective
physical world. Another assumption indispensable
for this objectivity is that of complete causality
in the macrophysical world. For if we had had to
reckon with the occurrences of effects not deter
mined strictly causally we could never have been
certain in our observation processes whether the
source of an effect we saw was to be sought in the
object we were observing or just in a cause-free
reaction of our observation instrument.
Thus objectivity would be disturbed if complete
causality did not exist; conversely, the representa
tion of objective physical events is a necessary as
sumption for the carrying through of the idea of
strict causality.
That complete causality is an indispensable as
sumption for the possibility of effecting the repre
sentation of objective physical events was already
clearly recognized by Kant. But there is no justifi
cation for concluding from this insight that the com
plete validity of the principle of causality through
out nature is guaranteed from the outset independ
ently of experimental experience. All that must be
established is this objectivity also is weakened
with the renunciation of complete causality. This
is actually the case in atomic physics; we have
seen that the principle of continuity can not be
given up without objectivity ceasing. And we have
learned that continuity ends in atomic and quantum
physics. We can consider the appearance of dis
continuities in elementary physical processes as the
fundamental proposition of modern quantum phy
sics; the atomistic structure of matter may be in-
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TWENTIETH CENTURY PHYSICS
terpreted as one facet of this elementary physical
discontinuity which also appears in many other
forms.
The above examples have already made it
clear that in quantum physics a complete causality,
of the type we are accustomed to, no longer exists.
But we still want to refer particularly to the differ
ence that exists between the quantum theory use
of the probability concept and the Boltzmann evalu
ation of it (for the kinetic explanation of heat pro
cesses). In Boltzmann's considerations statistics
was a secondary thing; at that time there was no
reason to doubt that the motion of each individual
atom could fundamentally be calculated precisely
in advance. The pursuit of such fine processes,
was voluntarily relinquished and statistical consid
erations were used as an expression of an incom
plete (but sufficient for the result desired) obser
vation of the events. Whereas in quantum theory
the primary natural laws themselves take the form
of probability expressions in this case the statisti
cal concepts are not an expression of the incomplete
ness of our insight into events, but rather an ex
pression of an indefiniteness existing in nature
itself. Nature herself did not determine indi
vidual atomic processes in advance; from case to
case she executes unpredictable decisions which
show fixed regularities only in the statistical aver
age. But these unpredictable decisions of nature
are always connected with elementary quantum
physics discontinuities. Indeed it is the indepen
dent cases of quantum transitions that are not
predetermined.
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TWENTIETH CENTURY PHYSICS
Our earlier example of the interference of light
for the screen with two openings already demon
strated that quantum physics must also relinquish
the idea of objective events.
With characteristic positivist modesty we limited
our problem to the problem of how great the pro
bability is that the light quantum in question will
be absorbed in a certain point of the photographic
plate. Thus two quantum transitions and that
is typical of the whole modern quantum theory
are placed in a static relation with each other. We
observe the quantum transformation of the light
emission from the point source; then we observe
the quantum transformation of the absorption of the
light quantum in a certain grain of the plate; and
we can theoretically calculate in advance the prob
ability of the occurrence of the second elementary
act after the incidence of the first. But we cannot
extend the picture of an objective event between
both processes in the form of the specification of a
continuous path which the light quantum must
traverse from the first position to the second.
Formerly one might have been inclined to sus
pect that the principle of the objectivity of physical
events was also inseparably connected with the
possibility of the quantitative, mathematical com
prehension of natural regularities. But we see that
that is plainly incorrect; everything we try to ex
plain here in words can be expressed in as mathe
matically clear a form as Galileo-Newton mechan
ics. We must replace the precalculation of future
events on the basis of complete causality possible
in the macrophysical domain by a purely proba-
126
TWENTIETH CENTURY PHYSICS
bility prediction. The probabilities of quantum
physics processes are themselves determined exactly
quantitatively; in the last analysis they are subject
to precise mathematical laws of great simplicity
and of the most comprehensive validity.
Despite that, the Kantian interpretation, that
complete causality (as well as objectivity and con
tinuity) of natural processes is an indispensable
provision of every physical thought in general, is
still correct in the following sense : quantum physics
experiments are also always performed with macro-
physical apparatus. We need macrophysical (thus
functioning according to strict causality) apparatus
to be able to make any correct observations at all
and to be able to determine regularities in the
atomic world. Classical physics remains the indis
pensable support from which an advance into the
world of quanta and atoms becomes possible. This
can not be altered by the fact that macrophysical
laws can naturally be interpreted as results of
quantum physics elementary laws. The laws which
govern the motions of macrophysical bodies must
naturally result from the laws to which their indi
vidual atoms are subject. There is no difficulty in
volved in the necessity of interpreting the strict
causality of macrophysical events as a result of the
purely statistical laws for the elementary processes.
For that is the essence of conformity to statistical
laws despite the incalculably of the separate
event, an exact, predictable result occurs in the
total effect of a large number of individual pro
cesses. The fact that we thus interpret the laws
of atomic physics as the really true natural laws
127
TWENTIETH CENTURY PHYSICS
from which macrophysical laws are derived as
results does not permit us to overlook the other
fact, that the elementary laws of atomic physics
include a tangible content only when they are
attached to the frame of macrophysics by concrete
application. Herein lies in the final analysis the
root of the not only historical, but contemporary
significance of the Bohr correspondence principle.
For this teaches us to understand the meaning and
content of quantum physics laws from their re
lation to macrophysics.
3. Complementarity. Experimental evidence
has shown us in a most comprehensive way and
with a variety exceeding all expectations the atomis
tic structure of all physical substrata; not only mat
ter, but also light (despite its wave nature which it
exhibits "on the other side") has a corpuscular
make-up.
This evidence drives us to remarkable conclu
sions. How can one observe and investigate indi
vidual atoms? We saw that modern experimental
technique permits the very satisfactory performance
of experiments immediately involved with indivi
dual atoms (and therewith to exactly prove the re
ality of these atoms, without a doubt). Naturally
experimental manipulation of individual atoms re
mains much more difficult and far different from
the investigation and measuring of macrophysical,
visibly large bodies which are made up of innum
erable atoms. For macrophysical bodies we have
scales and other mechanical, optical or electrical
measuring instruments at our disposal; but there
is a decisive difference for measurements on atoms.
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TWENTIETH CENTURY PHYSICS
We know that every physical substratum, therefore
every physical measuring instrument, is composed
of atoms be they material atoms or electrons or
light quanta. This destroys all possibilities of us
ing convenient measuring instruments for this re
search as is done for macrophysical objects or
events.
We have already considered how fundamental
for our classical physical ideas and methods of per
ception is the fact that in macrophysical investi
gations the back-coupling, the influencing of the
object by the observation process, can be made
negligibly small through the use of sufficiently fine
measuring instruments. But if we consider that all
measuring instruments themselves consist of atoms
(thus can never be made finer and smaller than
single atoms) we see that this method of eliminat
ing the reaction of the measuring instrument is
barred when the object to be investigated is itself
an individual atom (or a structure containing just
a few atoms). There is no longer any possibility of
investigating and observing with instruments
that are finer than the object in question. Nor
is it possible to control the influencing of
the object by the measuring instrument and
to eliminate it from the result by a corres
ponding conversion. Thus it must be con
sidered as part of the bargain that fundamen
tally measurments on atomic objects are always
"falsified" in the sense that according to natural
law the object experiences a variable interference
from the execution of the observation process.
Similarly when we try to observe and psychologi-
129
TWENTIETH CENTURY PHYSICS
cally control our own thought processes we are suc
cessful up to a certain degree; but the functioning
of the observation itself again influences the ob
served "object" our own thought process and
with this sets the limits for the possibility of ob
servation. (One can not, e.g, watch through psy
chological self-observation how one falls asleep,
because just that attention of observing prevents
one from falling asleep. Also, e.g., the origin
of voluntary decisions is disturbed and changed
by internal-controlling self -observation.) Similar
ities are also found in atomic physics the ob
served object is influenced by the observation pro
cess itself. With Niels Bohr we can say, the sepa
ration between observed object and observing sub
ject begins to vanish here.
It is not at all proper to call this influencing
of the object by the process of observation a "fal
sification". For we are not dealing with a disturb
ing influence which is in any way limited for the
present by the current deficiency of our observa
tion technique; these barriers to the possibility of
an ideal observation which does not influence the
object itself are limited through the atomistic
structure of physical foundations t>y natural law.
Therefore, we must ascribe to the atomic objects
themselves a certain character of "indeterminate-
ness", of "indefiniteness" of their physical be
havior which makes the construction of an
objective picture of atomic physical events impos
sible.
This need not imply that every possibility of
exact measurement on atomic objects is doomed to
130
TWENTIETH CENTURY PHYSICS
failure. It is possible throughout to make each
physical property of an atom the object of precise
measurements. If a certain property of an atom
is observed exactly there result from the observa
tion process (due to the reaction of the measuring
instrument to the object) strong uncontrollable
and undefined changes (strong "uncertainties")
with regard to other properties of this atom. By
optionally transferring the interference which is ne
cessarily associated with observation of the atom to
different properties of the object it is possible to
make accurate observations on the properties of the
atom undisturbed by the particular reaction. With
this "complementarity", as Bohr named it, the new
theory can eliminate those apparently hopeless con
tradictions we first encountered in the dualism of
waves and corpuscles and which we met at every
step in quantum physics.
This idea of complementarity must be viewed
as the most significant result for philosophy that
crystallized out of modern physics. It presents
an absolutely new scientific way of thinking which
is fundamentally different from classical scientific
thinking in terms of objectivized representations.
After the intellectual penetration and comprehen
sion of atomic physical phenomena completely in
accessible to the previous method of representation
became possible through it, it appears justified to
believe that it may further become of epoch-making
importance in other realms of natural science. The
enlightening force of this idea in solving an apparent
ly insoluble puzzle and contradiction is clearly
demonstrated in the famous problem of the dual-
131
TWENTIETH CENTURY PHYSICS
istic nature of light. The properties connected
with the wave nature of light on the one hand
and those connected with its corpuscular nature
on the other are "complementary" to each other
in the sense that they can never appear in one and
the same experiment at the same time (and thus
come into actual direct opposition). Experiments
which let the wave side of light emerge clearly
force (through the action that is connected with
every experiment) the corpuscular nature of light
back into the indeterminate and unobservable ; other
experiments, which force the corpuscular side of
light into prominence, leave undefined and indis
cernible all the properties which usually betray to
us the wave nature of light. With this wonderful
device of complementarity nature combines in one
and the same physical object properties and regu
larities that contradict each other so that they
could never exist directly at the same time.
Let us pursue this in somewhat more detail
in the already repeatedly discussed example of the
interference of light rays transmitted through
two screen openings. If we want to let the inter
ference of these two light rays take place to
illustrate the wave nature of light we must, as
already indicated, relinquish the desire to determine
simultaneously through which of the two openings
a definite light quantum was transmitted. We can
also consider this event from the "complementary"
opposite side. We can undertake to desire to
observe through which opening the light quantum
was transmitted. But then we must conversely re
linquish any desire to obtain an interference of the
132
TWENTIETH CENTURY PHYSICS
two rays. For with the latter intention the only
procedure we can follow is to roughly close up one
of the screen openings in order to be certain that
a transmitted light quantum could actually only
have passed through the other opening. There
is no experimental possibility of assuring ourselves
in any way through which of the openings the
light quantum was transmitted without simul
taneously so altering the conditions of the experi
ment that the interference of the two rays is
hindered.
As another example let us consider the charge
cloud of the electron in the hydrogen atom. If
we fix the position of a definite point with a micro
scope we must assume an inaccuracy which is at
least of the order of magnitude of the wave
lengths of visible light thus much larger than
an atom. But nothing hinders our imagin
ing that we have a microscope that is not depend
ent on visible light, but on X-rays or even rays
of much shorter wave length (gamma rays). With
this microscope we could accomplish measure
ments of position on an electron with such great
accuracy that positions inside of the charge cloud
of the hydrogen atom would also be distinguished.
Now let us place a hydrogen atom under this
gamma-microscope and "examine" the inner struc
ture of this atom so that we determine the posi
tion of the electron. In the description of this
imaginary experiment we must not forget one
thing; namely, that the energy of the "gamma-
light" necessary to illuminate and render the
electron visible is concentrated in individual light
133
TWENTIETH CENTURY PHYSICS
quanta which possess very high energy because
of the minuteness of their wave lengths. The
procedure of the "examination" of the electron in
the hydrogen atom is as follows: a single energy-
rich light quantum meets the electron, and reflec
ted by it approaches us through the microscope,
showing us the exact position of the electron. But
in this process the electron experiences a terrific
effect; it is thoroughly dislodged from its former
condition by the interaction with the energy-rich
light quantum and in most cases we can expect that
the electron is completely torn away from the
hydrogen nucleus; the atom, thus, is ionised.
We can now explain in a concrete way the
meaning of the "charge cloud" around the atomic
nucleus calculated according to wave mechanics.
We repeat the above described experiment in
numerable times; and, it must be emphasized, each
time we use a hydrogen atom which is in its lowest
energy state (normal state). If, instead, we took
atoms in a fixed, higher energy level we would
have to reckon with a different structure of the
charge cloud; for each of the different energy
levels, according to quantum theory, there exists
a certain specific structure of the charge cloud.
By repeatedly measuring the position of the elec
tron in a hydrogen atom in its normal state we
find the electron in different positions from case
to case, just as in our interference experiment we
found the individual light quanta in different
places on the photographic plate, statistically dis
tributed according to the light intensity calculated
by the wave theory. The statistical distribution
134
TWENTIETH CENTURY PHYSICS
of the individually measured electron positions is
given by the charge cloud calculated according
to wave mechanics. It was only with this deter
mination that the concept of this charge cloud
attained a clear meaning which is defined by con
crete, demonstrable experiments.
At the same time we see in this experiment how
the changing actions in quantum physical observa
tion are bound up with the observed facts. Be
fore the act of observation in question the hy
drogen atom possesses a definite energy, but in
general in these circumstances a definite position
of the electron does not exist the position of
the electron is undefined, or only indefinitely de
fined in the structure of the statistical charge
cloud. It is only through the process of observ
ing its location in the gamma-ray microscope that
we force the electron to assume a definite position.
Notice, we do not prescribe in which position it
should emerge; but we do force it into some
definite position and thereby force it to a new
crisis; now the electron assumes a definite position
but simultaneously an indefinite energy exchange
has taken place between the gamma light quan
tum and the electron and the original condition
of a defined energy of the atom has been dis
turbed.
A quite analogous process is represented by the
previously described impinging of a linearly polar
ized light quantum against a Nicol prism. In this
case we can also say that the execution of an act
of observation has forced the light quantum to
assume a clearly defined situation, when previously
135
TWENTIETH CENTURY PHYSICS
this was indefinite. The light quantum must de
cide whether to be transmitted by the Nicol prism
which has been placed inclined to the original
plane of vibration of the light quantum or to be
reflected by it. That is a decision of the same
kind as that of assuming a definite position forced
upon the electron in the above experiment.
It is obvious that there is no more place among
these ideas for a complete causality, clearly pre
determining each occurrence. If in a macro-
physical structure, the planetary system, for exam
ple, we want to pre-calculate future movements ex
actly we must know two things. First, we must
know that the Newtonian law is valid (and not
any other one), and we must know the magni
tudes of the different planets which are deter
minative for Newtonian gravitational attraction
and for the relations of force and acceleration.
Secondly, for any one point in time we must know
the positions and velocities the different planets
possess at exactly this point in time. Thereby
the general course of motion is mathematically
precisely determined for all later (besides, also
earlier) times. In an electron, however, we are
not able to simultaneously determine its position and
velocity at a definite point in time. Since position
and velocity are complementary, the position meas
urement in the gamma-microscope makes the velo
city of the electron unobservable and the con
verse also holds. After knowing that the physical
properties of an atom are partially complementary
to one another, that therefore it is impossible to
136
TWENTIETH CENTURY PHYSICS
observe the atom simultaneously "from all sides"
as it were (as is possible in macrophysical bodies),
it must be regarded as quite natural that pre
calculations of the future conduct of atoms, elec
trons and light quanta are not possible analogously
as in the planets. Let us emphasize once again:
this impossibility not only depends on a practical
technical incompleteness of our instruments, but
depends on nature itself. It is a positive result of
the natural laws which in quantum or wave me
chanics have attained a formulation which is
mathematically exact and is verified by innumer
able experiments.
As we saw, we can quite clearly recognize the
real root of this impossibility in the basic fact
of the atomistic structure of all physical founda
tion. The indefimteness inherent in the physical \
condition of all atomic * objects stipulates a cor
responding indefiniteness in the process of the
action; pre-calculation according to exact causal
laws is lacking here. The inability of the physicist
to predict for an individual case which of the
various possibilities will be realized in the quan
tum transition which is the basis for an observa
tion process is not due to human imperfection of
knowledge; nature herself has reserved until the
last the decision for each individual case.
Finally, let us make it clear that our repeated
use of the word "indefiniteness" in relation to
atomic physical events actually expresses nothing
but the impossibility of using familiar classical
concepts in the place in question. The itnpos-
137
TWENTIETH CENTURY PHYSICS
sibility of describing the relations in objectivised-
process pictures lends as many difficulties to the
verbal expression as does the problem of a clear
representation.
138
CHAPTER VI
PHYSICS AND WORLD OBSERVATION
L Natural Scientists and Philosophers. It is
natural that in the classification of the trends of
physical science, after they have been described,
the personal opinions of the author play a greater
part than they did in the brief summary of the
facts. It is desired that the reader recognize the
limitations imposed by this.
What has been developed in the preceding are
the modern, generally accepted conceptions of the
contributors to modern quantum and wave me
chanics which were derived from the experimental
work in this field. It should be emphasized that
some physicists (Planck, v. Laue, also Einstein)
consider these thoughts paths too revolutionary
and do not accept them as conclusive but still
cherish the hope that further development will lead
to a certain "restoration" of the older method of
representation through new experimental dis
coveries. But, in any case, these opinions are
purely personal and are based on uncertain future
hopes which find no support in the present state
of our knowledge. The author, therefore, is con
vinced that the new conceptions must be con
sidered conclusive new discoveries will at most
result in a more radical formation of the revolu
tionary tendency. Because of the force with which
the new concepts follow from the modern state
of experimental knowledge and its theoretical
139
TWENTIETH CENTURY PHYSICS
penetration it follows that the development of
these ideas does not belong to one person alone.
Its progressive clarification resulted with inescap
able necessity for us quantum physicists. I be
lieve that the views of Bohr and Heisenberg, to
whom the principal credit for the development of
these ideas is due, correspond closely with the pres
entation given above.
In the following effort to indicate the attitude
of the new physics to more general questions it
shall be our endeavor to limit ourselves to what
can be regarded as firmly and reliably established.
It shall be important for us in this effort to con
sider in what direction and how far the results
obtained by the new physics contributed to the
world problems affecting our times. We shall ig
nore all problems to which the answers do not
appear necessarily predesigned by these bases
also any questions regarding which the author's
personal opinion is very definite.
It is likely that this report has clearly indicated
that recently physicists were urgently directed
to the necessity of an epistemological philosophi
cal proof and contemplation of its function.
One would expect, therefore, that the relation be
tween physical and philosophical research would
have been especially close and strong; a more com
plete explanation of why this was not the case at
all is certainly deserved. The fact is that from the
philosophical point of view the new physics is
frequently regarded with scepticism or is chal
lenged. The philosophical criticism is limited mostly
to the alleged impossibility of the new thought
140
TWENTIETH CENTURY PHYSICS
paths and is based on the dogmatic designation of
the older concepts as the only possible and invar
iably necessary ones. This is connected with the
wide separation of the paths of the physicist and
the philosopher. In Aristotle's time all branches
of natural science were still branches of philo
sophy; but the further development which led to
the progressive independence . of the natural
sciences separated philosophers more and more
from natural scientific investigation. The fact
that most present philosophical study (quite dif
ferent than it was for Aristotle) is primarily
based on philological-historical studies and de
pends but little on contemporary mathematical and
scientific work 1 cannot contribute to promoting
fruitful relations between philosophical studies and
scientific research. The developments of modern
science make it more and more problematical what
subject realms of philosophical research, in gen
eral, could provide something of importance to the
natural investigator. All the problems amenable
to philosophical research in spiritual-scientific
spheres perhaps also in cultural, historical, socio
logical' and allied research lie beyond the bounds
of a natural scientific utilization of philosophy. In
our momentary consideration, that type of phil
osophy which, in general, cannot be interpreted as
a part of science, but whose character should be
denoted by the word "wisdom" is avoided
Nietzsche imagined such a philosophy, existing out
side the framework of scientific thought and ac-
1 The philosopher A. Wenzl, e.g., is a noteworthy exception;
but we cannot go further into his interesting explanations of
the new physics here.
141
TWENTIETH CENTURY PHYSICS
cordingly to be evaluated by quite different rules.
But what problems of specifically philosophical
nature are related to natural scientific research?
The increasing independence of natural scientific
branches from philosophy from Aristotle's time to
the present has simultaneously also emptied phil
osophy of its original content and problems. Up
to our time the opinion has remained that it is the
task of philosophy to clarify certain "final" and
most general questions of natural science; ques
tions which concern perhaps the "existence" of
matter, or the "existence" of time and space, or
the "existence" of force, or the "final" bases of
"existence". The development of physics, how
ever, shows clearly that no useful suggestions for
natural investigators are to be anticipated from
such endeavor. With the possible exception of at
tempts to investigate the results and thought proc
esses of natural science with regard to their rela
tion to spiritual or non-scientific problems the only
possible modern philosophical work which will be
useful and fruitful for natural investigators must
concern the theory of the method of natural
scientific thought for example, the questions of
the theory of knowledge. The present status of these
problems indicates that their fruitful treatment
can succeed only in closest contact with the fore
most front of natural scientific investigation; the
extensive research devoted to the theory of knowl
edge from the philosophical point of view for the
most part stands too far from modern natural sci
ence and its actual problems.
Because of this condition physicists were led
142
TWENTIETH CENTURY PHYSICS
to reflect upon the most profound questions of
physical knowledge in their own way; and from
experimental evidence, which no one could anti
cipate a few decades ago, they were led to develop
answers, the inescapability of which can only be
exactly understood on the basis of more certain,
superior knowledge of these experiments,
We have shown in previous chapters that the
philosophical concepts developed by the phys
icists themselves were influenced essentially by
Machian positivism. For that reason all the phil
osophical speculation whiclTreferred to the "exist
ence" of nature, of matter, of space, of time or
of force was eliminated. Clarity could be at
tained and hopeless complications and contradic
tions be removed only through the very determined
and disrespectful (one might almost say brutal)
insistence on the principle that a scientific declara
tion possesses true content and sense only in so
far as it expresses relations and regularities in the
material of our experimental experience. The de
velopment of this principle requires careful analy
sis of all propositions. We saw that the proposi
tion that two certain events occurred on the earth
and on Sirius simultaneously required penetrating
analysis, the results of which finally led us to
new, unexpected conclusions. It often happens
that just such propositions which we are wont
from long habit to use without further analysis
are actually shown to require analysis on the basis
of positivist criticism. We saw, In relativity and
in quantum theory, how our most habitual forms of
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TWENTIETH CENTURY PHYSICS
representation and methods of judging had to be
revised.
Basically every proposition can be subjected to
penetrating analysis. For each assertion, as we
usually state it, can be reduced or resolved into
other assertions which are more directly dependent
upon experimental determinations and events.
Here there is no final limit of analysis. (This
point was not estimated quite clearly and correctly
by Mach.) For just this reason analysis and critic
ism on the basis of epistemology can and
need not work in a vacuum; it must not accept
just any proposition and argument (it would lose
itself in the endless thereby), but it must by its
analysis and explanation establish the domain
where the actual and fruitful problems of scienti
fic research lie. It is the task of the instinct of
the successful scientific worker to find the places
where perceptive criticism is necessary and promis
ing; only the practician in research work can guide
the considerations of epistemology in fruitful direc
tions.
2. The Liquidation 'of Materialism. The new
concepts, resulting from the experiences of quan
tum physics and their intellectual interpretation,
mean a far-reaching liquidation of the classical
western world picture developed by natural science
from the Greek materialistic philosophy. The
opinion has been expressed that the new develop
ment is not a "surmounting" but rather a "refine
ment" of the materialistic world picture. But in
a certain measure it is a matter of taste whether
one speaks of "surmounting" or "refinement".
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TWENTIETH CENTURY PHYSICS
Kant's philosophy also could be considered either
as surmounting or refinement of the materialistic
world picture according to one's taste; and the re
visions introduced into Kant's theories by rela
tivity and quantum theory can be called a refu
tation as well as a continuation of Kant's concep
tions. That depends upon wliich part of a theory
one wishes to consider the essential nucleus and
which part as the external part, capable of further
development.
The problem is only clarified when it is indicated
to what extent the new perception is different from
the old one. Actually by comparing the new
physics with the materialistic world picture one
can determine that today just those theses of the
materialistic conception of nature which expressed
the conflict between materialistic theories "and
other ideas are antiquated.
Compared to the lucid and tangible (and be
cause of this clarity so stimulating and fruitful
to natural research) representation of materialistic
atomic theory, modern atomic physics is essentially
more abstract. Our description will already have
demonstrated that; but let us once more indicate
a few essential features of modern knowledge in
which this more abstract nature of modern atomis-
tics emerges. Democritus' atoms were indestruc
tible and invariable; modern "elementary particles"
on the other hand are capable of unlimited trans
formation. Thus a neutron can (in a radioactive
"beta-process") be transformed in such a way that
three new particles result from it: a proton, an
electron and a particle ("neutrino") of a type
145
TWENTIETH CENTURY PHYSICS
not previously mentioned, that assumes, as it were,
a position intermediate between electron and light
quantum. The proton, in turn, can likewise be
resolved into three particles; namely, a neutron,
a "positive electron" (that also exists), and again
a neutrino. Positive and negative electrons can
mutually "compensate" for each other in such a
way that there remain only one or two excess light
quanta; conversely, negative and positive electrons
can again be produced in pairs out of light quanta.
Analogous processes certainly exist for the proton,
although they have not yet been observed ex
perimentally. Light quanta can disappear com
pletely through absorption in atoms, or conversely,
can be produced anew.
In Democritus' representation each individual
atom had a definite destiny and possessed in its in
destructibility and invariability the permanent
guarantee of its lasting identity; while the elec
trons and other elementary particles of the modern
physicist, aside from their destruction and con
version properties, possess no individuality. The
meaning of this determination has been amply ex
plained above.
Finally, the existence of atoms is no longer a
primary basic fact of nature; it is only a special
part of a much more general and comprehensive
phenomenon the phenomenon of quantum dis
continuities. Whereas we dwelt at first on the
historical development of the atomic concept and
then recognized quantum eff ects as phenomena as
sociated with these atoms, the logical and modern
interpretation is just the reverse. The basic
146
TWENTIETH CENTURY PHYSICS
fact' is the presence of something which abso
lutely defies verbal expression and clear repre
sentation and can only be approximately indicated
by the term "discontinuity". This elementary dis
continuity, characterised by the Planck quantum
of action and amenable to a complete, quantitative
comprehension in mathematical formulae, is re
vealed among others in the somewhat clear fact of
atomistics. We became familiar with the dualism
of waves and corpuscles; we know that under cer
tain circumstances nature is revealed in a form
corresponding to the simple atom representation;
but we also know that it can be revealed from
other angles and that then the elementary discon
tinuities appear in other forms.
The atom, or electron, as we know it today, is
therefore completely different from Democritus'
atoms ; and again it could be designated as a ques
tion of taste whether atomic physics in its modern
state is to be regarded as a "refined" confirmation
or as a radical refutation of the ideas physicists of
the last century entertained about atoms. Democri-
tus had declared all the "qualities" of color, of
smell and taste or heat an illusion and ascribed to
atoms as true properties only those of bodily form
and motion. But Mach had already spoken out
against the prevailing physical ideas in his,posi-
tivist criticism. The assumption that qualities had
to be ascribed to atoms as we perceive them with
the sense of sight and the sense of touch is pre
cisely as arbitrary and superfluous as would be the
assumption that the qualities of color or musical
pitch had to be ascribed to them. The new de-
147
TWENTIETH CENTURY PHYSICS
velopment added justification to Mach's criticism
and raised the importance of the geometrical pro
perties against other qualities. The atom, as we
know it today, no longer possesses the tangibly-
clear properties of Democritus' atom but it is
stripped of all sensual qualities and can only be
characterised by a system of mathematical
formulae.
The unbridgeable conflict of materialistic phil
osophy and positivist theory of knowledge is es
pecially sharply prominent on this point. For
with this determination one of the most prominent
features of the materialistic world picture is con
clusively liquidated; at the same time the positi
vist theory of knowledge is confirmed and deci
sively verified.
People today frequently advance Ernst Mach's
challenge to the atomistics of that time as dis-
proven by later experiments ; and Mach's estima
tion, unsuccessful as stated, of the most significant
problem o physical knowledge is often introduced
as a basis of proof against positivist perception
criticism in general. But these arguments are
obviously based on a completely obsolete and anti
quated conception of "microphysics" j the proposi
tion that our experiments had confirmed the reality
of atoms could in this rough form only tem
porarily, in the first quarter of this century, be
considered correct For the information described
in Chapter Two, which first appeared to confirm
the basic idea of Democritus, stands in contrast to
the quantum phenomena, treated in Chapter Three,
which forced us finally to a very different evalu-
148
TWENTIETH CENTURY PHYSICS
atlon of the total condition. From a really triodern
standpoint the older idea o the atom must be
regarded as just as much disproven as confirmed,
since the corpuscular concept considers only one
side of the picture, neglecting the other comple
mentary side. If the quantum theory strips the
atom of its clear tangible qualities and leaves only
a framework of mathematical formulae for its char
acterization, our theory of knowledge attitude is
confirmed again physical research aims not to
disclose a "real existence" of things from "behind"
the appearance world, but rather to develop
thought sytems for the control of the appearance
world. The atom, characterized only as a frame
work of formulae, is, similar to the earth's geo
graphical degree net, after all only a framework
for the classification of experimental facts.
Of equal importance philosophically is the
surmounting, brought about by the new physics,
of "fatalism", which had reached complete develop
ment in classical physics. In the last century it was
imagined that the motions of atoms were regulated
by laws similar to those controlling motions in
the planetary system so that all nature in each
very fine detail is like a ticking clock, whose run
from the very first to the most recent times is prede
termined with absolute mathematical strictness. This
method of representation was depicted by DuBois-
Reymond with fascinating clarity. Imagine a
thinking spirit that is infinitely superior to us in
quantitative capacity, but qualitatively possesses
the same thinking ability as we. He has the abili
ties of a "complete" mathematician; i.e., he is able
149
TWENTIETH CENTURY PHYSICS
to complete calculations in a fraction of a second
which would occupy all the mathematicians of the
world for a thousand years. Besides, through ex
periment and observation he knows the condition
of the world in every detail at a definite point in
time; he knows where each atom was at that time
and how great its velocity was. Then this "La
place spirit" would know everything which human
savants could ever know. For him all future events
are completely calculable in advance. Likewise
he can see back into the past ; his calculations advise
him of every unexplained crime and every lost sec
ret action. Every human cerebral fibre, past and
future, is known to him precisely and he can calcu
late every human action.
The new physics declared the thus illustrated
scientific world picture as plainly erroneous. We
know now that there can actually be no question of
pre-calculable determining causality of all atomic
processes. Though this causality and ability to
calculate really exists in the planetary system,
in microphysics of atoms and quanta something
new and unpredictable may happen at any time.
This determination deserves special attention in
regard to living organisms. It was impossible for
the manner of representation explained by DuBois-
Reymond to imagine that the strict causal prede
termination of all atomic motions should suffer an
exception in the human brain; in logical conse
quence man had to be explained as a complicated,
mechanical automaton. The strong opposition of
this thesis, 'Thomme machine" to the religious
world was elaborated with especial joy by the bel-
150
TWENTIETH CENTURY PHYSICS
ligerent representatives of materialism.
By now we know that we can only refer to an
exact, predetermining causality in the realm of
macrophysics ; we must consider whether living
organisms are also to be added to "macrophysics"
in this sense. Every living organism, even the
smallest, is indeed a powerfully large structure in
comparison with an atom; but that is not sufficient
reason for designating it as a "macropyhsical"
structure. For the characteristic of an inorganic-
macrophysical body is that at times it contains in-
numerabe atoms which are of the same sort and
are subject to the same external conditions; here,
and here only, can complete causality over the des
tiny of the macrophysical body be assumed as a
result of the statistical laws to which its individual
atoms are subject. In the living body the state of
affairs is entirely different; for all parts of the
living body exhibit wonderfully fine and most high
ly complex developed structures. The discovery
of the microscope made the fulness of these com
plicated structures acessible to us ; but they continue
down below the limits of microscopic visibility,
certainly in part down to "colloidal" and molecular
dimensions. Correspondingly, the quantities of
matter which take part in certain very fine, but
decisively important physiological reactions appar
ently often embrace only a few molecules.
Most primitive physiological experiences teach
us that reactions involving large exchanges of
energy and chemical substance are controlled by
other processes which are much finer. Consider
that in the higher animals (vertebrates, arthropoda)
151
TWENTIETH CENTURY PHYSICS
the "macrophysical" muscular motions are control
led by the nervous system, by much finer processes
which occur in the brain and other nerve centers.
The supposition appears justified that similar re
lations occur in many forms in organic life; and
there is basis for the conjecture that the "final"
controlling relations are of absolutely atomic-phy
sical fineness. Thus one knows, e.g., that the light
sensitivity of the eye extends down to a few indi
vidual light quanta. And heredity research, which
shows that individual organisms are composed
mosaically of their hereditary factors, raised to the
surface as a quite general regularity an elementary
discontinuity in the variation of the heredity fac
tors. Obviously here we are also approaching the
atomic and quantum physical discontinuities of
elementary events.
If the supposition is correct that the controlling
reactions of organisms are of atomic physical fine
ness, it is evident according to our modern know
ledge that the organism is quite different from a
machine and that its living reactions possess an
element of fundamental incalculability and unpre
dictability. One can object that our fundamental
understanding of life phenomena is not greatly
aided by considering a statistically functioning dice
cup instead of a machine as the pattern of the
organism. But at the moment it is only important
for us to determine in the negative sense that the
machine theory of organisms (including their fur
ther results; e.g., in the sense of a denial of the
freedom of the will) can hardly exist in view of
the new physics. Bohr, who vigorously expressed
152
TWENTIETH CENTURY PHYSICS
his conviction of the fundamental importance of
the new physics for the problems of biology, saw
a difference between quantum physics and biology
in that in quantum physics we study the statistical
behavior of individual atoms under well, defined con
ditions, while the internal conditions in living
organisms may no longer be definable in atomic
measure so that here still closer limits are imposed
on observation than in atomic phsyics. The new
concept of complementarity, which resulted from
quantum physics as a new scientific thought form,
must according to Bohr be of fundamental impor
tance for the investigation of life processes inde
pendently of all knowledge of atomic physics. It
is a fact, familiar to every man, that all attempts to
investigate more precisely the inner conditions of
a living organism are narrowly limited if one wants
to avoid (completely or partially) killing it These
limits will gradually be extended considerably by
the discovery of better observation instruments.
But it is obvious to suppose that limits will exist
for that that here also a fundamental complemen
tarity relation exists, which appears to be a charac
teristic of the living. In atomic physics we learned
to interpret the process cf observation as a power
fully active interference on the observed object; in
the living organism this undissolvable combination
of determining observation and disturbing interfer
ence is shown most strikingly.
These indications suffice to show what a wonder
ful perspective the new physics opened up for bi
ological research. The idea of complementarity,
developed in atomic physics to a conclusive idea
153
TWENTIETH CENTURY PHYSICS
structure, made it possible to reconcile the confi
dence of our hope in a deeply penetrating natural
scientific comprehension of life processes with the
conviction that the characteristic of the living
lies in its ability to deprive itself of the defining
objectivization of its internal conditions.
3. Positivism and Religion. For centuries the
natural sciences supplied the sharpest weapons to
anti-religious movements. Since the anti-religious
movements in Europe today seem to have passed
their high point and are beginning to be dissolved
due to opposing currents, it is a pressing demand
of the time to recheck the relation of the natural
sciences to religion and to determine whether the
anti-religious belligerent attitude of the natural
sciences, culminating in HaeckeFs time, is still pos
sible today.
A test of these questions will have to examine
the noteworthy ideas which Bavink explained in his
"Contributions and Problems of the Natural
Sciences", 1 and which were more definitely repre
sented in a smaller book to which he gave the
characteristic title, "Natural Science on the Way
to Religion". 2 The great success of these publi
cations shows that Bavink's thought processes
coincide essentially with the desires and needs
of the present time; and I wish to state that this
readiness to accept his ideas, according to my con
viction, need not correspond to a temporary fashion
trend. Bavink developed the concept that, in op
position to earlier, materialistic science, modern
1 Fifth edition, Leipzig, 1933.
2 Second edition, Frankfurt a. M. f 1933.
154
TWENTIETH CENTURY PHYSICS
development of science is pressing toward a re-
erection of the religious world picture.
Bavink's conclusions about the liquidation of
the materialistic picture of nature are doubtless
essentially correct. But we do not want to over
look the importance of a very careful proof of
the problem in accord with the religious importance
of this determination. The difficulty of the prob
lem results from the fact that the religious world
picture itself is not conceived as fixed in all its
details but as progressively developing and chang
ing. Consequently it isn't at all certain which
scientific theories "contradict" religion. For ex
ample, consider that before Copernicus and Colum
bus hell was beneath the earth and the kingdom
of heaven was above the stars. The knowledge
that the earth is a sphere and Copernicus' theory
of its motion thru interstellar space strongly op
posed the former ideas. A retrospective, cultural,
historical consideration leaves one hardly any
doubt that the reversal on this point has taken
part of its vitality and persuasive power from re
ligious doctrine by forcing a more abstract formu
lation of its conceptions. Despite these, no one
today, any more than at that time will consider
these natural scientific theories as a contradiction
to the religious concept world. The various pos
sible religious evaluations of natural scientific or
philosophical theories are also shown in the ex
ample of Kant's philosophy. It stands in very
sharp opposition to previous philosophical systems
which rested more closely on theological concepts
and tried to support and confirm these in me&a-
155
TWENTIETH CENTURY PHYSICS
physical constructions. Kant declared the "me
chanistic" world picture (i.e., the idea and repre
sentation world of materialistic philosophy in the pre
cise form obtained through Newtonian mechanics)
to be the only possible basis for natural science.
Thus he severed all possibilities for a knowledge
of God based on a metaphysical interpretation of
nature. Bavink properly underscored Kant's close
positive connection with the materialistic or "me
chanistic" natural philosophy a relation often lack
ing sufficient emphasis. In his important work on
the "History of Materialism" Friedrich Albert
Lange presented Kant's philosophy dually as a
"refinement" and as a "surmounting" of the ma
terialistic world picture.
Kant himself testified to the deep impression
made on him by the study of Newton's works, ad
vancing the so-called "Nebular Hypothesis" of
the origin of the planetary system. He taught
admittedly in a hypothetical construction that not
only present planetary motions result from New
ton's laws with complete causal certainty, but the
origin of the planetary system from an original
chaos of nebular matter was also to be imagined
as a scientifically understandable process on the
basis of Newtonian gravitational attraction.
Therefore Kant extended and progressively inten
sified the representation of the planetary system
as a clock ticking according to law, requiring no
regulatory supervision by the world creator so
that the origin of the planetary system is also to
be understood according to natural law without
the intervention of the creator. "Nous n'avons pas
156
TWENTIETH CENTURY PHYSICS
besoin de cette hypothese", declared Laplace.
But while on the one hand Kant explained that
a mechnical consideration of nature was the only
possible form of scientific thought, on the other
he made the materialistic philosophy "innocuous"
by severing from it its metaphysical conclusions
(in the anti-religious sense) by a very shrewd,
grand thought process. He declared, namely, that
the mechanical world picture of natural science was
necessitated simply by the invariable thought
forms belonging to the human mind; our inter
pretation, the mechanical world picture, is not de
pendent upon nature itself; the compulsion for this
idea results from the internal design of our mind.
Consequently the character of nature is not ex
pressed at all in the basic theses of the mechanical
explanation of nature, and the usual evaluation of
these basic theses in metaphysical conclusions in
the sense of the materialistic anti-religious phil
osophy is impossible.
That Kant, in carrying through this develop
ment, actually unjustifiably made the basic concep
tion of Newtonian mechanics absolute could only be
clearly recognized later, after the creation of rela
tivity and quantum theory. Until then the prob
lem of science and religion could have been viewed
as satisfactorily solved since by recognizing un-
Umitedly the mechanical world picture as a thought
form of natural science, religious metaphysical con
cepts had attained a position for natural scientific
thinking and conclusions which was absolutely not
assailable. From the standpoint of Kantian ideas
it could be declared that there was no occasion for
157
TWENTIETH CENTURY PHYSICS
religious thinking to consider it desirable or sig
nificant to replace the mechanical picture of nature
by another one.
But actually historical development proceeded so
that Kanfs philosophy could not prevent material
ism in any way from radically completing its own
anti-religious metaphysics. Haeckel and his allies
simply did not recognize the position Kant had
given to religion and drove the battle for unlimited
materialism further with philosophically gross but
propagandistically effective thoughts and catch
words. Actual historical development forces us to
the conclusion that Kant's surmounting of ma
terialism in its very abstract character could not
permanently obstruct the anti-religious movement.
This consideration must induce us to agfee uncon
ditionally with Bavink in his idea that the modern
liquidation of the materialistic, mechanistic pic
ture of nature signifies a positive gain in freedom
of motion for religious thinking.
An important distinction between Bavink's ideas
and the theories of modern physics is yet to be
established insofar as Bavink spoke out tem
peramentally and definitely against the positivist
conception of the character of physical knowledge;
positivism is unacceptable to Bavink. Or rather,
let us say that until now it has appeared unac
ceptable to him, for Bavink, who shows a ready
disposition towards new natural scientific develop
ments has openly revised many details of his ideas ;
thus, it is perhaps not out of the question that his
opposition to positivism might yt be changed in
the future to a closer connection with the general
158
TWENTIETH CENTURY PHYSICS
convictions of modern quantum physicists.
For and this should again be underlined posi
tivism is not a private affair. Naturally it is not
dependent on the word "positivism". Every ac
tive investigator will claim the individual right to
assume his own position in the finer shadings of
epistemological methods of interpretation. But
there is an epistemological conception, basically
absolutely unif orm> among modern quantum phys
icists and one cannot reject this conception of
modern physics without also rejecting quantum
mechanics itself or in any case regarding it as
still unfinished and unexplained. The necessity of
this conclusion is also absolutely recognized by the
above mentioned physicists (Planck, v. Laue, also
Einstein) who reject "positivism" and conse
quently do not recognize modern quantum physics
as conclusive but hope for a restoration of the
"mechanical", strictly causal picture of the world.
Bavink, who for his part welcomes the surmount
ing of the mechanical world picture, through his
rejection of positivism turns against the new
physics which effected it. We must regard them
as inseparably connected; the new physics is not
conceivable without the influence of the positivist
perception theory; conversely, positivism was first
stabilized and rendered precise with the replace
ment of thinking in objective processes by the new
thought form of complementarity.
The endeavor to escape positivism is essential
for the manner in which Bavink chose to find in
modern science a confirmation of religious doc
trines; he wanted to find a direct road to a posl-
159
TWENTIETH CENTURY PHYSICS
tive recognition of God through the penetration
of the secrets of nature. This approach is closed
for the positivist attitude because positivism fun
damentally disputes the possibility of collecting,
classifying and describing observation facts them
selves with our knowledge. Positivism denies
every possibility of a natural "character percep
tion". The radical rejection of the materialistic
philosophy to which positivism leads is a result of
just that positivist criticism which denies to mater
ialism the characteristic assertion that the "charac
ter" of all things has been found in matter.
Thus in this direction we cannot follow Ba-
vink. But not only is the resultant liquidation of
materialism an important enough result, but also
the positivist conception offers new possibilities
of granting living space to religion without con
tradiction from scientific thought. Let us remem
ber that positivism accepts experimental observa
tions and experiences as the sole "reality" for the
physicist. The emphasis on this concept leads
us to the fact that there are experiences possible
which are quite different from those observations
and results classified in the physicist's system. As
long as the objectivity of all physical phenomena
appeared unopposed and self-evident one could try
to ascribe to the products of this objectivization,
to the objective physical events in time and space,
a sort of "higher" reality than to the direct observ
ation experiences themselves. But after we have
just learned differently here, we are no longer
forced to place physical experiences in opposition
to the small fraction of all human experiences
160
TWENTIETH CENTURY PHYSICS
which depend on the measuring instruments of the
physical laboratory or observatory. Let us re
turn to the problems we considered when we said
that the physicist represents blue light by a wave
motion of a definite wave length (or today also
by a stream of quanta of definite energy) . At that
time we already warned against the manner of
expression which was common in the pre-positiv-
ist times of natural science the assurance that
now the "character" of blue color is recognized
and the direct sensation of blue in Democritus'
sense is unmasked as pure opinion. The logical
execution of the positivist conception must estab
lish that "blue" as such is simply an accepted ex
pression; but there are further possibilities of in
ducing various other phenomena out of the blue
light by using certain refined apparatus ; and these
phenomena are of such great interest to the phys
icist because there are various properties to meas
ure in them. These phenomena to be expected
from the use of the apparatus in question can be
qualitatively predicted with all the details of the
measurements to be performed on them by the
wave theory, or, if quantum physics experiments
are to be performed, by the complete, dualistic
quantum theory of light.
This reformulation, necessitated by positivism,
of equal importance among the different possible
experiences, may in its further analysis become
very essential to the clarification of the problem
of the mutual relations of scientific knowledge
and religion. We want to emphasize a few
points which may have definite importance
161
TWENTIETH CENTURY PHYSICS
in this connection. First, let us remember that
in the above philosophy we already introduced
a distinction between a philosophy which tries
to make scientific assertions and one we
designated it as "wisdom" which strives to
make no scientific assertions but nevertheless "ex
presses" something very valuable. Thereupon it
was rightly pointed out that a Mozart sonata also
"expresses" something which cannot be converted
into scientific statements but the value of which
is not harmed by this. There do exist things
which can be expressed otherwise than scientifi
cally; and the positivist striving for a clarifying
cleaning and purging of our scientific system of
expression of metaphysical assertions which mis
take the limits of the character and' capacity of
scientific ability to think, places us in so much
greater readiness to recognize the importance of
other, possible non-scientific expressions in addi
tion to it
It was impressively shown by the famous psy
chologist, C. G. Jung, that not only the rational,
scientific perception function of our consciousness
but also the condition of our subconscious deter
mines our total attitude toward the world. One can
so denote the rationalistic free-thinking age, that
it fundamentally scorns and disregards the con
sciousness against the involuntary psychical
courses; we know from the modern psychology of
the involuntary how much such a procedure must
be avenged, since the "displaced" strivings of the
involuntary do not lose their force but become
condemned to a disturbing and destructive abnor-
162
TWENTIETH CENTURY PHYSICS
mal function. But against the involuntary psy
chical courses the non-scientific forms of expres
sion are just as important as the scientific expres
sions of our conscious thinking.
We have intentionally placed several different
considerations loosely beside each other without
wanting to enter into a more detailed investiga
tion of their mutual relationships. We do not
wish to solve the problem here, but are merely
trying to indicate it; the existence and import
ance of non-scientific forms of expression and
spiritual relationships is likely to be of essential
importance for the understanding of non-scientific
independence of religion.
It is inherent in the character of these fortps
of expression that we must relinquish the desire
to reach religious intelligence from the direct pur
suit of natural scientific knowledge. That, how
ever, does not diminish the religious importance
of the turning point which occurred in natural
scientific thought. For it is only with the positi-
vist liquidation of materialism and limitation of
the suitability and significance of scientific
thought as well as the positivist limitation of the
importance of physical measurements that we gain
that balance in the evaluation of our different
forms of experience that permits returning their
due place to non-scientific experience and ex
pression possibilities.
Such determinations do not comply with the
demands of religious theories since religious
thought also requires the right of existence for a
163
TWENTIETH CENTURY PHYSICS
special science theology. 1 But the tendency, pro
minent in earlier times and still evident today, of
relating the theses of this science to philosophical-
metaphysical thought paths is incompatible with
positivist criticism. Positivist criticism will only
admit to the theses of theological theories a mean
ingful content when they are shown on closer
analysis to be expressions of concrete experiences.
This interpretation may be unwelcome on many
sides; but it probably contains the indication of
a direction which could lead to a conclusion and a
new comprehension of lost religious insights much
sooner than is attainable from the simple "ac
cepting" of abstract theses. For example, one
could consider that the thesis, present in most
religions, of the world creator which interpreted
as a quasi-natural scientific expression has under
gone a progressive weakening of its content
through the development of natural science pos
sesses a very live meaning in the form of the
determination of an unbridgeable difference be
tween the "created" nature and the technique dis
covered and "made" by the people. This is a
theme of vital importance to us children of a
technical world; and there are voices present to
day which see a specific religious problem in our
relation to the technology.
But here we have reached the point where the
author, who speaks here only in his proper posi
tion as a physicist, must resist the temptation to
spin further the threads of the thought begun
1 "Theology" here means any striving for systematic religious
thought development without limitation to Christian theory.
Thus, in this sense, each developed religion possesses its theology.
164
TWENTIETH CENTURY PHYSICS
on his Own justification. To many a reader it may
possibly seem disappointing that we should halt
right now in our wandering and should leave the
final and most moving problems hanging in sus
pense. But if it is characteristic for philoso
phers not to want to rest without having found
the conclusive solutions to all problems in a se
parate "system", there belongs to the natural
scientist another attitude which Newton expressed
as follows: "I do not know what I may appear to
the world, but to myself I seem to have been
only like a boy playing on the seashore, and di
verting myself in now and then finding a smoother
pebble or a prettier shell than ordinary, whilst the
great ocean of truth lay all undiscovered before
me."
Thus let us be happy to see that the thoughts
have come in the stream and that the gates of
new developments are open. The attainment of
new natural scientific methods of representation
of complementarity means the maturity and con
clusion of an epoch of the richest gains for the
understanding of atomic and quantum physics. But
the evaluation of the new thought processes out
side of physics in the problem of biology and the
thinking through of philosophical and religious
questions still stand at the real beginning; their
results are not to be disregarded. Let us be
happy that our ship has weighed anchor for a
journey to new shores.
165
APPENDIX
I. COSMIC RADIATION
In 1912 V. F.-Hess In a balloon ascension dis
covered a remarkable radiation which falls onto
the earth from outer space. Numerous further in
vestigations have since been devoted to this pheno
menon. The first steps of the further investiga
tion were only slowly obtained; around 1924 the
reality of the phenomenon was still absolutely
doubted by outstanding physicists. For the prob
lem involves a radiation which not only remains in
visible to the eye but is also inacessible to the
perception of all rougher physical instruments;
only the extremely refined research methods de
veloped for the investigation of radioactivity the
Wilson cloud chamber and the counting tube
permitted the proof of the indubitable presence
of cosmic radiation and allowed a more precise
investigation of its nature.
The further the advance in these investigations,
the greater became the number of unsolved prob
lems presented by this radiation; but the greater
became also the stimulation to pursue this peculiar
phenomenon. In recent years cosmic radiation Has
become one of the increasingly important fields of
research in physics. Observations and measure
ments were gathered on sea voyages and through
expressly equipped expeditions from Spitzbergen
to New Zealand and Tierra del Fuego over all the
oceans because it appeared desirable to determine
the strength of incident cosmic radiation over the
166
TWENTIETH CENTURY PHYSICS
entire surface of the earth. Measuring instru
ments were carried up high mountains e.g., on
the Alps and the Peruvian peaks to see how this
radiation behaves up there. Piccard's famous bal
loon ascents were devoted essentially to the meas
urement of cosmic radiation at great heights; they
were exceeded by far by the recording balloon
ascents carried out in Germany and America. In
these latter, self -registering measuring instruments
were carried in unmanned balloons up to heights
of 20 km. and more; they showed that at these
great heights the intensity of this atmosphere
radiation, not yet weakened by passage through the
earth's atmosphere, is about 200 times greater
than at sea level. In other investigations the
measuring instruments were submerged in deep
lakes for hundreds of meters; there they meas
ured the smallest traces of radiation which pene
trate down to these depths and which belong to
an especially penetrating portion of this radiation.
Still other investigators descended into mines for
observations on atmosphere radiation.
A main goal of these investigations was to gain
information about the origin of cosmic radiation.
It is certain that it approaches the earth from
outer space; but we know almost nothing posi
tive beyond that. It definitely does not come from
the sun; and the conjecture, entertained for a
long time, that it somehow came out of the milky
way also had to be abandoned. For then the
motion of the milky way over us (as it results
from the rotation of the earth) must cause
periodic changes in the strength of the atmos-
167
TWENTIETH CENTURY PHYSICS
phere radiation to be recognizable; and experiments
show reliably that such is not the case. So they
had to resolve to assume the origin of cosmic
radiation in the depths of world space far beyond
the milky way. There have been attempts to com
bine definite occurrences in stellar development
with the production of this radiation; but these
are still of a very hypothetical and uncertain
nature. Meanwhile we must be satisfied with
exact information from the abundant investiga
tions which were instituted about the arrival of
cosmic radiation at the earth's surface and its
passage through the atmosphere. The puzzle of
its cosmic origins remains unsolved.
The arrival of cosmic radiation on the earth
is complicated because the radiation consists of
electrically charged particles. These are deflected
by the earth's magnetism into complex curved
paths which are difficult to follow mathematically.
The relations present are similar to those associa
ted with the electrons (coming from the sun)
which cause the northern lights. These problems
can be designated as extensively clarified.
The penetration of the earth's whole atmos
phere which cosmic radiation must accomplish be
fore it reaches the earth's surface would not be
possible if it did not possess a penetrating ability
that is enormously large in comparison to that of
X-rays (and to the radiation of radioactive sub
stances). Thus, lead plates which Completely
screen off radioactive or X-radiation are almost
no hindrance to cosmic rays. This tremendous
penetrability is due to the fact that the indivi-
168
TWENTIETH CENTURY PHYSICS
dual particles of cosmic rays are exceedingly
energy-rich. With the most modern technical tools
electrical potentials up to a million volts can be
produced; with these potentials very high velocities
(thus very high energies) can be imparted to elec
trically charged particles protons or alpha-parti
cles, for example. The particles in the radia
tions of radioactive substances possess energies
of similar magnitudes. But the particles of cos
mic rays have energies naturally not equal for
all the particles which extend to over a million
times this magnitude!
Cosmic rays, thus, give the physicist a unique
opportunity, formerly not attainable in any way,
to investigate the behavior of particles of enormous
energies. The field of research opened up thereby
is for the present inexhaustible; we repeatedly
discover the most remarkable, most surprising
things there.
One of the most beautiful findings was the (p.
146 briefly noted) positive electron ("positron").
Formerly electrons were known only as negatively
charged particles ; positive charges appeared to be
found only in atomic nuclei. In cosmic rays ap
proximately as many positive electrons were dis
covered as (fast) negative ones.
These positive electrons do not appear on the
earth as permanent constituents of matter because
they can be mutually annulled by negative ones.
In the closest combination of positive and nega
tive electrons their charges neutralize one an
other since they are opposite and both particles
disappear leaving only an indestructible quantity
160
TWENTIETH CENTURY PHYSICS
of energy, possibly appearing as a light quantum
(or in another form of energy). Conversely, the
production of a positive and a negative electron
can occur from collision between energy-rich
particles or by the close passage of an energy-
rich light quantum and an atomic nucleus. Such
processes occur over and over in the atmosphere
which cosmic rays traverse.
The energy-rich particles which can progres
sively tear off electrons from the air molecules they
pass can therefore cause ionization; occasionally
they also impart a large amount of energy to one
of the loosened electrons. But mainly the rapidly
moving electrons expend very large amounts of
energy in the form of very energy-rich light quanta
by rushing closely by atomic nuclei; these quanta
in turn produce more electron pairs.
Collectively these relations become very compli
cated and it is understandable that a complete dis
entangling of the state of affairs has not yet
been successful. It is not quite clear what type
the primary particles of cosmic rays really are;
almost all of the particles present therein are in
deed only secondary, or tertiary, or ... etc., pro
duced by successive processes.
Under certain conditions e.g., if we pass the
cosmic rays through a lead plate several milli
meters thick this production of electrons (posi
tive and negative) from energy can occur to such
an extent that a whole shower of newly produced
particles several hundred or even a thousand of
them spray out from the same, or almost the
same, point of production in the lead plate. This
170
TWENTIETH CENTURY PHYSICS .
remarkable phenomenon has already become the
subject of much careful research. The progres
sive theoretical treatment of the data gathered
thereby will yield important insights into the most
profound, unopened natural laws of matter; in a
certain sense these are nowhere as clearly and
characteristically expressed as they are for very
energy-rich particles.
Even before their experimental discovery (An
derson, Kunze) the existence of positrons was
predicted on the basis of the profound theoretical
considerations of the Englishman, Dirac; a theo
retical prediction, which, when it was made, ap
peared so bold that most physicists refused to be
lieve it at the time.
Since then, these processes of the destruction and
production of electrons thus material particles
have been experimentally checked and investigated
in all directions. Fundamentally they show clearly
that the elementary particles of matter, .the proof
of the existence of which meant such a wonderful
triumph of Democritus' ideas, in the final analysis
are quite different from Democritus' atoms. The
simplest, final elementary particles of matter are
not at all, as Democritus dreamed, impossible to
create and indestructible elements of all events.
If they are really incapable of any internal change
in condition they can still both appear and disap
pear. To be sure this has only been shown above
for the lightest material particle, the electron; it
is also valid for the heavier material particles, as is
briefly intimated at the conclusion of these con
siderations.
171
TWENTIETH CENTURY PHYSICS
We have mentioned (p. 82) a recently dis*
covered, previously unknown elementary particle,
the so-called "neutron" (Chadwick). It is very
similar to a proton, especially since it has almost
the same mass ; but it has no electrical charge and is
neutral. The great German physicist, Heisenberg,
had made it clear that all atomic nuclei are built
up of protons and neutrons. But our already
tremendously extensive experience with nuclear
transformation processes (element transmutations)
shows a proton can be changed into a neutron,
and conversely a neutron into a proton. The
transformations proceed spontaneously in radio
active substances without our aid; they can be pro
duced in many other nuclei by "bombardment"
with very energy-rich particles. Each time this
transformation takes place, besides, an electron
(positive or negative) is produced anew, and also
a "neutrino", a particle of still little-known nature.
Possibly such particles also play an important part
in cosmic radiation.
If we add to what we learned about the funda
mental dualism of waves and corpuscles our
Icnowledge of this ability of material particles to
appear and disappear in the most variable man
ner and not to be absolutely, indestructible we
recognize that the picture drawn by modern physics
is quite different from that to which Democritus
and the atomistically trained physicists of the last
century were accustomed. Neither atoms nor
their building stones, electrons, protons, neutrons,
are the invariable permanencies in the change of
physical phenomena; they are temporary forms of
172
TWENTIETH CENTURY PHYSICS
the indestructible we learn to know in physics
energy. The appearance of this energy in the
form of corpuscles, material, elementary particles
or under other circumstances in the form of its
complementary, wave side is only a specific case
of a much more general, much more comprehensive
and much deeper regularity; namely, the elemen
tary discontinuity that controls all quantum physi
cal occurrences.
What is concerned in cosmic rays, the puzzle
of its cosmic origin, became more mystifying
the more clearly it was recognized how energy-rich
many of the cosmic radiation particles are. At
present it appears impossible to understand by what
kind of processes such energies can be imparted
to an individual particle. Recently a very astonish
ing answer to the problem of the origin of cosmic
radiation attracted considerable attention; an
answer, which of course is purely hypothetical,
possibly also incorrect, but which in any case
points out a possibility to be considered seriously.
According to it, the source and origin of cosmic
radiation which rushes through outer space is not
to be sought in events that are still taking place
in the universe today; it is a remnant of energy-
rich radiations, no longer being produced but only
gradually being consumed, which were formed in
the ancient, original explosion out of which the en
tire universe arose.
II, THE AGE OF THE WORLD
The discovery of radioacivity shortly before the
end of the last century not only furnished the
173
TWENTIETH CENTURY PHYSICS
physicist with revolutionizing knowledge, it also
made new methods and experiments possible for
other fields of science.
We explained above (p. 107) the law of decay
followed by radium wherever it may be; the same
law is valid for other radioactive substances, only
the rate of decay differs. This radium disinteg
ration is a process taking place in the nucleus of
the radium atom. Whereas usual chemical reac
tions as processes which concern only the loosest
electrons in the electron shells of the atom in ques
tion can be strongly influenced by temperature
and pressure it is impossible to obstruct or ac
celerate the decay of radium by such means. Ruth
erford was the first to artificially produce a nuc
lear transformation (element transmutation) ;
since then physicists of the whole world have been
working effectively on the investigation of arti
ficially formed nuclear transformations. But such
abnormal means are necessary bombardment
with very energy-rich individual particles to pro
duce them that one can say that apart from nuclear
physics laboratories and occasional effects of cos
mic radiation non-spontaneous nuclear transfor
mations never occur on or in the whole earth. We
must add that the rapid alpha-particles emitted by
radioactive substances occasionally can meet an
other nucleus and induce in it a transformation
Rutherford's experiment involved just such a proc
ess; but that happens so seldom that it is insig
nificant in our present discussion. Since cosmic
radiation can produce effects (which could attract
the geologist's attention) only as great as the nuc-
174
TWENTIETH CENTURY PHYSICS
lear physics laboratories we see that all radio
active substances present in the earth's crust with
its different geological strata decay at exactly the
same rate as they do in a laboratory; and they
not only maintain this rate today, they have kept
it all the millions of years the earth has existed.
There was also the reliability of being able to
subject this conclusion to a direct empirical check
by observations on minute radioactive inclusions
in rocks which have become faded from the radia
tion that passed within very close range of each
of these inclusions through the course of millions
of years; details, that naturally we can not depict
and explain more extensively here, permit a check
on whether a rate change took place in the course
o millions of years or whether perhaps (this was
naturally very conceivable) radioactive substances
existed in earlier periods of the earth's history that
we are not familiar with because they long ago
decayed to what are at present imperceptibly small
residues. Actually, neither the one nor the other
is the case.
If a quantity of radium enclosed in a rock de
cays at an invariable rate, one can later figure
out how much time has elapsed since the radium
became enclosed in the stone on the basis of a
determination of how far the decay has pro
ceeded. Therefore accurate investigations were
performed to determine the extent of the already
completed decay on all stones containing radio
active substances within them which could be ob
tained; from these it was possible to calculate how
long ago the stone in question had been formed*
175
TWENTIETH CENTURY PHYSICS
It Is remarkable that somehow such "stone clocks"
occur In almost all geological layers; their ticking
had proceeded uniformly throughout the millions
of years of the earth's history and all its revolu
tions and permits us late-comers on this earth to
read off today the age of the various geological
strata.
Geological Age in
Time Period Millions of Years
Neozoic Group
Mesozoic Group
Paleozoic Group .
Proterozoic
Precambrian .
Archeozoic
Azoic .
176
TWENTIETH CENTURY PHYSICS
On the opposite page there appears a sum
mary of the results (from a compilation by (X
Halm) ; for each of the large groups of geologi
cal epochs there are several separate values listed
for older and younger stone layers.
In general how old is the word? We see from
the table that the oldest known geological layers
are about one and a half billion years old. The
age of the earth is therefore fixed as still greater
than this number; but it is improbable that it is
much more than triple this value.
It was possible to extend this age determina
tion still further. It can be assumed that the
earth was once formed out of the material of the
sun; a spiritually rich idea of St. Meyer's shortly
afterward showed the possibility of learning some
thing about the age of the sun from terrestrial
radioactivity investigations; the result is that a
certain period of time, which to be sure does not
embrace the entire lifetime of the sun, but a large
part of it (perhaps half) can be very exactly spe
cified as 4.6 billion years.
That is a very remarkable result. It might well
have been expected that the great sun were a much
older inhabitant of the universe than the small
earth expelled from it; but as we see, that is not
the case at all. No less remarkable are the results
of age determinations on meteors which likewise
became possible through radioactivity investiga
tions. It was shown that these fragments of the
universe which, it is partially demonstrable
(through path observations), perhaps do not be
long to our solar system to begin with, but are
177
TWENTIETH CENTURY PHYSICS
hurled at us from further distances of interstel
lar space, are never essentially older than the sun
and earth.
Here we meet problems before which we humbly
perceive the limits of our research ability. Physi
cal information is obtainable to a certain degree
by executing planned experiments. But meteors
from outer space do not appear at our order;
here we see scarce material that has been placed
at our disposal by the favor of conditions and
that increases only slowly. But despite that, who
is to hinder us from reflecting over our present
findings? And who will dispute that a careful
consideration of the findings thus far can be stimu
lating and fruitful for our further research?
If we summarize our knowledge up to the pres
ent, we must say that we have found no body the
age of which was shown to be higher than 10,000,-
000,000 (10 billion) years. There is no basis for
believing that in the gigantic milky way system to
which our sun belongs stars are present which
are essentially older. And in addition there is no
basis for ascribing a higher age than that of the
milky way to the "spiral nebulae", analogous to
our milky way, which lie far outside of our milky
way system in space the oft described Andro
meda nebula is the most familiar example. Is
there, therefore, in general anything at all in
space which essentially is older than ten billion
years ?
To approach this problem from a still different
point of view; the American astronomer Hubble
stimulated again by certain theoretical consi-
178
TWENTIETH CENTURY PHYSICS
derations (de Sitter) with the tremendous in
struments which stand at the disposal of Amer
ican observatories, determined a fact which is
very simple to express. Its proof was not as
simple as the formulation of the result. An in
dispensable assumption for its proof was a major
achievement of modern astronomers the deter
mination of the distance of the spiral nebulae simi
lar to our milky way.
With a stereo telescope, the two optic fora
mens of which He on two points of the earth's
path opposite each other, we can see a part of the
stellar sky stereoptically. Instead of the stellar
sky perceived by our eyes, in which the stars are
little light-points very far apart we would see the
planets as spatially very close and many fixed stars
as farther away but as yet thoroughly estimable
lights with regard to their separation from us.
But most of the stars of our galaxy and all the
more naturally the spiral nebulae beyond will ap
pear to this enormous stereo telescope as im
mensely distant as to a pair of common human
eyes.
Astronomers actually work now with such a
stereo telescope; only naturally they must wait
a half year between the views (or photograph
ing) through the one and then the other optic
foramen until the earth has carried us from a
point on its path to one opposite it. In this way
the distances of the closer fixed stars can be de
termined reliably. But how is it possible to make
these determinations on distances which are still
quite small for astronomical measure. It must
179
TWENTIETH CENTURY PHYSICS
suffice here to say that it became possible; in
genious uses of the fact that there are certain
"classes" of fixed stars which show (according to
observation) simple relations between absolute
luminosity and other easily observable properties
have made it possible to see still deeper into space
than the earthpath-stereotelescope ("parallax
determination") reaches. That was only the first
step; others followed in a bold structure erected
by the astronomers with enormous care and pre
cision. Gradually the entire milky way became
extensively "transparent" to us in such a way that
we see quite well the spatial division of its stars
and star clusters. Meanwhile a final step was exe
cuted; distance determinations were made possible
for the more distant world islands beyond the
milky way system, the spiral nebulae. Here they
determined, as mentioned before (p. 32), distances
up to 100 million "light years" (and considerably
more) .
Since there also existed well founded estimates
of the total mass of such world islands, it is pos
sible, by calculations on the spiral nebulae met up
to a certain distance, to determine by laborious sta
tistics how great the central mass density of the
universe is. It is unusually small in the statisti
cal average only 1 x 10~ 80 (a one divided by a one
with thirty zeros after it) grams per cubic centi
meter.
It is very important that this could be deter
mined. Previously we touched quite briefly
(p. 50) on certain knowledge concerning which we
are spiritual heirs of the German thinker Bern-
ISO
TWENTIETH CENTURY PHYSICS
hard Riemann one of the greatest mathematicians
o all time. Riemann had discovered that the
laws of Euclidean geometry which are in no way
logical necessities independent of all physical ex
perience permit a generalization which can be de
signated as the utilization of the principle of a
field of force in geometry. Even before physics
had arrived at the field of force principle Riemann
had introduced it (without actually using the same
name) into geometry. We have already mentioned
that these Riemann ideas form the support and
mathematical scaffolding for the attempt to grant
to the gravitation law also (analogous to the elec-
trodynamic laws) the form of a field of force
law. Full utilization of Riemann's ideas leads to
the fact that space must not necessarily as is as
sumed by Euclidean geometry be infinitely large.
Mathematically spaces having definite finite
volumes can be represented without requiring the
presence of walls or some other boundaries to
close them off. (This can be explained by a simple
example which has only one fault, that of being
a two dimensional structure, a surface, whereas
Riemann's theory refers to three-dimensional
space. The surface of a sphere notice that we ac-
. tually mean the surface and not the volume of the
sphere has no boundary anywhere, despite which
it is only finitely large, i.e., contains a fixed num
ber of square centimeters.)
Knowledge of the gravitation constant 1 and
mean mass density of the universe, touched on
* This refers to the so-called relativistic gravitation constant,
8ir//c2 where / is the Newtonian gravitation constant and e is
the velocity of light.
181
TWENTIETH CENTURY PHYSICS
above, makes it possible to calculate the size and
total mass of the universe. These calculations
were first performed on the basis of more diffi
cult, more complicated theories, the definitive char
acter of which can perhaps be doubted. But if
only an approximate orientation, not too exact
numerical values, is required it can be shown that
the numerical values desired are quite simple to
ascertain through considerations which are quite
independent of all the still doubtful refinements
of gravitation theory. Fantastic as it may seem
the (approximate) value of the total mass of the
universe, to be considered of finite size, is known
1 x 10 55 (a one with 55 zeros after it) grams.
The "diameter" of the universe, the greatest se
paration which can exist between two points A
and B in the universe, is also known. (If one
goes farther from A in any direction, in every
case the separation from B decreases. It is the
same as on the earth's surface when a man who
has traveled to the south pole always comes closer
to the north pole with each step he takes in what
ever direction.) This diameter is approximately
ten billion light years.
Finally we want to mention the Hubble dis
covery. If we spectroscopically resolve the light
coming to us from a distant spiral nebula we find
that it contains spectral lines we know; thus the
same laws of atomic physics hold in the farthest
reaches of space as here. But these spectral lines
exhibit a considerable Doppler effect we al
ready know (p. 42) what that is which be
comes more pronounced the farther away they are.
182
TWENTIETH CENTURY PHYSICS
All these distant spiral nebulae are conceived of
as in rapid flight; the velocity of which is propor
tional to the separation of the nebula in question
from us.
What does this mean? We have indicated that
a very close connection grew up between geometry
and physics from the profound Riemann ideas.
Now direct support for this relation must be
found. Since the flight of distant nebulae is a
quite general phenomenon existing not only in
single examples but (as far as our knowledge
extends) in general in all known nebulae, and, as
mentioned, follows a uniform regularity this neb
ula-flight must be interpreted as an explosion-like
growth of world space itself. The universe it
self is expanding with furious velocity and thus
the separations between the world islands con
tained within it are increasing proportionately.
The numerical value which is determinative for
all flight velocities (velocity of a nebula divided
by its distance) is exactly such that one arrives
at the determination that the diameter of the uni
verse is increasing directly with the velocity of
light. That is not alone and of itself a very ra
tional result which can consolidate essentially our
confidence in the correctness of our whole con
sideration. But it also yields a further result.
Let us look back into the past; the world dia
meter, growing with the velocity of light, was
formerly smaller than it is now; if we mentally
pursue the development of the universe farther
and farther back, we come to a point where every
thing is at an end, or rather, everything is at
183
TWENTIETH CENTURY PHYSICS
the beginning. About ten billion years ago the
world diameter, today grown to ten million light
years, must have been vanishingly small. So by
a very different path we return to the determina
tion empirically arrived at from age determina
tions; ten billion years ago Lemaitre especially
deserves credit because of the closer execu
tion of this representation the initially small
universe arose from an original explosion. Not
only atoms, stars and milky way systems but also
space and time were born at that time. Since then
the universe has been growing, growing with the
furious velocity which we detect in the flight of the
spiral nebulae. . . .
It is remarkable that modern natural research
gives rise to knowledge and ideas which drive
our feelings in such different directions from
those of natural research from the times of La-
mettrie to Haeckel. It is doubtless very justi
fiable for the author of a modern book on the
mathematical theories of relativity and cosmology
to pronounce at the conclusion that our scientific
research on the future and past of the universe
need not be influenced by human desires and hopes
or by theological theories of creation. It is also
characteristic that the state of development of our
science suddenly makes such warnings necessary
again.
But when we pay just recognition to this warn
ing, when we don't allow any motivation for our
scientific research other than the inexorable striv
ing after the knowledge of truth, who would hin-
184
TWENTIETH CENTURY PHYSICS
der us afterwards from once dreaming about the
results achieved?
And certainly this picture of the universe as
exploding fireworks which went off ten billion
years ago invites us to consider the remarkable
question of Miguel de Unamuno, whether the
whole world and we with it be not possibly
only a dream of God; whether prayer and ritual
perhaps be nothing but attempts to make HIM
more drowsy, so that HE does not awaken and
stop our dreaming.
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